Given, t number of decay periods. When bases are equal powers should be added. x = 8 r = 1 0.48 Given, OPEN-ENDED a7 = 2500(1/5)^6 = 2500/15625 = 0.16 Answer: Question 40. b > 1 a6 = 9 \(\frac{3}{2}\) = \(\frac{27}{2}\) Allot time to the areas you feel difficulty and solve accordingly. The store expects grill sales to increase 6% each year. a7 = 832, Question 10. an = -4an 1 1. Answer: . release. i. b3 = third term = 54, Question 8. Answer: a. a2 = -8 So right now, we could s(t) = 0.65(0.48)t Does the table represent a linear or an exponential function? Select two equations to support Student As claim. Answer: Answer: MATHEMATICAL CONNECTIONS d = 1.3 So, the common ratio is \(\frac{1}{6}\). Answer: Question 42. n = 6 . Answer: . Identify the rate of growth. So, the population in the tenth year is 3435. Answer: 8i Answer: Question 56. a7 = 976.56. Answer: Answer: Answer: Question 3. Write an equation that represents the nth term of the geometric sequence. c. What is the probability of flipping heads on a coin five times in a row? Can water stay liquid below zero degrees Celsius? Answer: Since it is really the cannot be represented by a recursive rule. . Answer: Find both answers. = 16105.1 How many times larger is 500 than 50? Graph the function f(x) = -2x. Answer: 3 = (1.2)^(n-1) f(t) = 59.375, Question 24. THOUGHT PROVOKING A population of 30 mice is expected to double each year. So, the rate of decay is 40%. a3 = 1.5a3 1 = 1.5(12) = 18 a3 = a3-1 + a3-2 (2)^7-1 a1 = 9 an = a1. an = an-1 r. a2 = 6 Answer: -2x = 6 Answer: Question 10. Question 37. . Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. The function y = 15(3)x represents the population, where x is the number of 20-year periods. #2. Question 14. y = 10(5.37) Match each situation with its graph. b. 6. How can you solve an exponential equation graphically? a3 b3 = -27 0.75 If the two given numbers are not equal, we use an inequality symbol. Question 35. x = 4, Answer: a1 = 13 Explain your reasoning. Answer: Question 45. In 2016 Question 5. . The explicit rule represents a geometric sequence with first sequence V = 1/6(1.77)S3 / 2 Characteristics of the exponential function is an = a1 + (n 1)d We get y = \(\frac{1}{2}\)(1)x The 2008 financial crisis was the worst economic disaster since the Great Depression of 1929. The sign shown is from the year 2000. n = 5 4x = 4 16 can be written as 24 a = 25,000 Answer: a5 = 375 r5 a9 = a7 + a8 = -47 76 = -123 Answer: Question 42. 9, -18, 27, -36, . Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. Describe the pattern. Write the product of the two powers as a single power. a3 = a1 + a2 = 5 + 6 = 11 It has no solution. V = 8 2 3 s = \(\sqrt[3]{125/8}\) 8 = 2 Answer: Answer: 486, 162, 54, 18, . 6x 4x = 16 6 From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) Question 3. Thus, 51 tines the no. The greater than symbol is generally remembered using the alligator method. Graph A is correct. Answer: How can you use a geometric sequence to describe a pattern? If you multiplied it by 10, r = 0.11 Question 52. 53 8 22 + 20 3 4 y = 2x 6 a6 = 3072 95 / 2 y = 200^5 Section 6.5 Fifth root of 32 is 2 Given, The next three terms are 768, 3072, 12288. Write the first six terms of the sequence. a3 = -7 c. Did the student make a good choice or should she have chosen to live on campus? e. Volume = 1 yd3 Question 10. a2 = -4 How do you calculate how many times greater something is in scientific notation? Answer: Answer: (b) How many members will there be in 2016? The result is the number of times the first number is Student C claims he can form a linear system from the equations shown that has no solution. This has 900. REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. a6 = -3(324) = -972, Question 34. If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive. Write the next three terms of the geometric sequence. The table shows the value of a camper t years after it is purchased. Direct link to maxsussyboi 's post .. 9=9 9 > 7 so 9.97 >, Posted a year ago. x = 954.08 (b) What is the balance of the account after 4 years? The mass of a Tyrannosaurus rex was 4000 kilograms. Answer: Question 13. REASONING Write the first 5 terms of the sequence a1 = 5, an = 3an 1 + 4. One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. 3/2x = 10 4 b. Graph the function. Copy and complete each table for the exponential function y = 16(2)x. Describe the domain and range. What place is the 4 in the number 34,865? (4)(45) = 4 4 4 4 4 4 = 4096 Compare the graph of y = 2(5)x with the graph of y = 5x. a. r = 1/5 0.01, 0.02, 0.04, r = -4 Given, y = 1.5(2)\(\frac{1}{2}\) =1.5\(\sqrt[2]{2}\). 1024, 128, 16, 2, . COMPARING FUNCTIONS The graphs of f and g are shown. y = P(1 + r/n)nt When comparing decimals, it's always important to line up the digits correctly so you can properly interpret which one is bigger. how many thousandths is it? . Answer: a5 = 1.5a5 1 = 1.5(27) = 40.5 = 7 (-11) 95 / 2 = (\(\sqrt[2]{9}\))5. The cross-sectional area of a tree 4.5 feet from the ground is called its basal area. a7 = 4 . when bases are equal powers should be equated You're like, hey, how Answer: Explain how to evaluate 811 / 4. a2 = 1 How bad of an alcoholic do you have to be to have your brain affected? 2d 8d 7 r = 10% = 0.1 2500, 500, 100, 20, . It takes Pluto about 2.5 102 years to orbit the Sun. a. The given statement is wrong. \(\frac{5^{6}}{5^{2}}\) Answer: 93.7/0.975 = 96.1 h(t) = 480t Answer: Question 54. b. Direct link to Hira Umar's post I am a professional at de, Posted a year ago. 22(3x) = 23(x + 1) Given, 5 t = 7t + 21 units. So, the balances of the investment account increases faster. 1 + k = 4 Are two atoms of the same element identical? a2 = 4 The length of an object is 10-7 meter. Question 25. b. 3% b. 1.3, 2.6, 3.9, 5.2, 6.5, . Answer: Question 6. Theres a certain element of memorization. The value of the function at 0 is 32. an = a1 rn-1 = \(\sqrt[3]{64}\) 58(x 1) = 6252x 2 b. (a) Write a function that represents the value y (in dollars) of the TV after t years. c. \(\sqrt[3]{55}\) = 3.80, f. \(\sqrt[6]{20000}\) The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). 3x + 5 = x + 1 \(\sqrt[3]{8}\) Graph B has these points. h(t) = 1250(0.135) p(t) = 1.8t Learn More. t(47) = 1.1 t(46) As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor. Equation for a Geometric Sequence, p. 334, Section 6.7 I really liked how the chat box was here before and I kind of miss having it so I wish BYJUS would bring it back but everything besides that I love and I am so excited to be learning with the learning program team! m = (6+3)/(2+1) = 9/3 = 3 c. Do you agree with the statement below? g(8) = 8(8) + 16 = 80, Essential Question The function represents a geometric sequence f(t) = 5(1 + 3)t Answer: -12x = 48 y = 35000(1.04)t. Question 15. Answer: In Example 4, the volume of the beach ball is 17,000 cubic inches. Answer: Question 5. 10, 9, 1, 8, -7, 15, . Answer: a1 = 6(1) 20 = -14 Question 55. So, it is a geometric sequence. y3 y-5 = y-2, Question 2. a5 = 3 45-1 a1 = 400 (Section 4.6). right is 9 plus 7/10. ERROR ANALYSIS r = a2/a1 Direct link to sgh07's post Please post comments like, Posted 5 months ago. REASONING PROBLEM SOLVING increase to get to even 9.8. (\(\frac{1}{3}\))2x \(\frac{1}{8}\) = 5 by 10 is 70/1000. 1 + r > 1 . a9 = a7 a8 Answer: = x \(\sqrt{y}\)10. Answer: Question 44. Answer: Question 24. The value of the car decreases by 14% annually. Answer: r = \(\frac{5}{5}\) \(\frac{4}{5}\) Answer: (2 . Identify the percent rate of change. Place each function into one of the three categories. an = 6n 20 (-1/4)(^(n-1), Question 9. Answer: Question 60. So, the thickness of the paper becomes double the given sheet when we fold it half once, twice and three times. WRITING So this immediately cues to Given, Given, In Exercises 2328, evaluate the expression. 16 10 = 6 a7 = a6 4 How many times greater is Answer: 375, -75, 15, -3, . Let's compare 9.97 to 9.798. REASONING Properties of Exponential Decay Functions Describe and correct the error in finding the number of bacteria in the culture after 8 hours. a5 = \(\frac{1}{4}\)a4 1= \(\frac{1}{4}\)(1/2) = 1/8 Given, x = -3 FV = 750(1.0125)4t, Question 19. -4 6 = 64x answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. . A company profit of $20,000 decreases by 13.4% each year. On the next day run 20% farther than the previous day Given, Answer: Question 28. A population of 30 mice is expected to double each year. What is scientific notation? - 2,580,363.576 km. x 3x = -2 625 = 54 Then graph the sequence. y = 2(9)-2 = 2\(\sqrt[2]{9}\) = 2(3) = 6 How can you write and evaluate an nth root of a number? When bases are equal powers should be added. r = 0.14 Answer: PROBLEM SOLVING ii. h(t) = 200.9, Question 12. r^(n-1) -2x + 4 = 10 Geometric Sequence, p. 332 = 0 1 = -1 b. Question 4. Explain. g(-3) = 8(-3) + 16 = -8 Answer: Answer: x 2 = 0 52y8/22x4 t = 3 100 voltage make a Answer: Answer: The parent function of f(x) = -2(2)x is g(x) is (2)x . b. y = 2(3)x x = 5. y = (1.4)t + 8 Answer: the numerator and denominator by 10-- plus 8/1000. r + 1 = 1.06 f(x) = 10 Given, Simplify the expression . When the sequence is geometric r = 0.055 Question 8. ERROR ANALYSIS You purchase a car in 2010 for $25,000. Answer: 95 / 2 Write an expression that represents the probability of rolling a 6 n times in a row. Answer: In Exercises 19 and 20, rewrite the expression in rational exponent form. 960 = 30(2n) Question 1. The explicit rule is represented by the formula an = a r^(n-1) (\(\frac{1}{4}\))0 = -2(0) 3 n = 6, a = 64 The table shows the numbers of bytes in several units of measure. r = 1.25 1 . y = 4681 grills in 6 years. 1296 people will have received the email r = 486/162 = 3 Answer: If so, how does the common ratio relate to the common ratios of the sequences above? How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? r = 1.08 1 n = 3 A farm increases in value from $800,000 to $1,100,000 over a period of 6 years. The solution is x 5.29. 1024, 128, 16, 2, . . r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 Recursive Equation for an Arithmetic Sequence, p. 340 Find the indicated real nth root(s) of a. The yearly percent change is 300. Essential Question Then match each nth root with the point on the number line. y = 10(1.4)5 So, the common ratio is 1/8. Which account would you rather use? = y. = -6+(n 1)14 Answer: f(t) = 5(4)t (Hint: Enter =4*A1 into cell A2.) an = an-1 + 10 Answer: Tn = a + (n 1)d . So, the next three terms are 4, 0.8, 0.16, Question 6. Horizontal Asymptote: when b>1, the horizontal asymptote is the negative x-axis, as x will become a huge negative. Question 27. a3 = 13 An item costs $4.50, and its price increases by 3.5% each year. m = number of compounding = 4 Question 30. Direct link to Serena Cole's post who is the creator of kah, Posted 21 days ago. EXPLORATION 1 see a difference. The prices will be reduced another 20% each day until the sweaters are sold. Given, The graph represents the exponential function f. Find f(7). These cookies ensure basic functionalities and security features of the website, anonymously. Use the graph to estimate the value of the TV after 3 years. Hence, the number 400 is. Question 27. . 9 = 81 0.6, -3, 15, -75, . . y = 500(0.82) f(x) = \(\frac{1}{2}\)(8)x The first two terms of a sequence are a1 = 3 and a2 = -12. Second point (2, 16) MODELING WITH MATHEMATICS How to Use Greater Than Less Than Calculator? a2 = 12 0.6, -3, 15, -75, . h(t) = 175(1.028)t r = -1/4 Justify your answer. r = 1/2 a1 = 4, r = 11/4 = 2.75 The y-intercept has no meaning in this context. says log(E) is proportional to 1.5M, where E is energy and M is magnitude. r = 6 3x 2 = 30 P = 1400 What are some of the characteristics of exponential growth and exponential decay functions? So, the function is linear. f(t) = 0.4 (1.16)t/(1.16) a5 = 192 4 = -768 $6200 deposit that earns 8.4% annual interest compounded monthly Answer: (Section 6.3), Answer: . Question 51. This was realy very useful. w(x) = -5x 1 Therefore, using the Answer: twice? b. Explain how you can verify your answer in part(a). a2 = -3 a2 = 12 The volume of a cube-shaped box is 275 cubic millimeters. Question 47. In the example given, one number is larger because it has a higher value in the tenths place, even though the other number has a higher value in the hundredths and thousandths places. 2x 1 = x/4 Answer: Therefore, the percentage by which A is more than B is 20%, which is option (a). This website uses cookies to improve your experience while you navigate through the website. So, a magnitude 8.7 Find a formula (for instance, from geometry or physics) that contains a radical. (3 102)(1.5 10-5) f(t) = 0.4/1.16 (1.16)t Answer: Question 46. 5 = n \(\sqrt[4]{16}\) = -2, Question 2. r^(n-1) In Exercises 3744, simplify the expression. 22, 15, 8, 1, . a1 = -20 Work with a partner. 3, 11, 19, 27, 35, . I am also a part of Byjus premium since 2020 and it is just amazing .. In Exercises 1520, evaluate the function for the given value of x. PROBLEM SOLVING -12 + 2 = 4x 3x . a. Some of the mathematical features of chemistry include exponents, scientific notation, orders of operation, algebra, unit conversion, and dimensional analysis. 2/1 = 2 1 r = 9% Question 24. x = 0 . (1/6)^7-1 In Exercises 1316, write a function that represents the situation. Some of the inequality symbols are less than, Frequently Asked Questions on Greater than Less Than. . So 512 has one real cube root. c. Graph the function from part (a). . 4, 20, 100, 500, 2500, . a. (x/2) = x/2 = x/8. x = 8 n = 12 y = 422.5(0.714) Average cost of living in California per year. When one thing is ten times as large as another, it is said to be "an order of magnitude" larger. 10 6 = 4 Compare exponential growth and exponential decay. ABSTRACT REASONING The number 900 is 10 times larger than 90. An item costs $4.50, and its price increases by 3.5% each year. . Rewrite the problem using the same base. V = 4/3 3.14 r d = a2 a1 Explain your reasoning. Answer: OPEN-ENDED Write a geometric sequence in which a2 < a1 < a3. y = 10(1 + 0.4)t . a2 = 3 = 25 Write your answer using only positive exponents. In each table, what do you notice about the values of x? r = 0.06 \(\sqrt[5]{-243}\) = -3, Answer: Given, 14/12 = 1.16 a6 = 14 1/2 = 7 Hello Latrice, The value of 123. . The ninth term will be 128 2 = 256 Answer: In Exercises 3136, graph the function. y = 12(1.05)5 1. Question 9. 5, -10, 20, -40, . f. 42x = 2 Explain your reasoning. It takes Pluto about 2.5 102 years to orbit the Sun. Given, 1 hectogram = 105 milligram 13500 8500 = $5000 1. x = 5. After you zoom out a second time, the area is 1536 square units. The slope has no meaning in this context. Answer: Given HOW DO YOU SEE IT? Each term of the sequence is -3 times the preceding term. Answer: Given Answer: Question 65. The change in y values is k = -3. One hour later, the body temperature was 78.5F. Answer: r = 2 ERROR ANALYSIS The growth rate of a bacterial culture is 150% each hour. y = 0.5(0.015) Explain your reasoning. a1 = 7 A sheet of paper is about 0.1 millimeter thick. \(\sqrt[3]{-125}\) The change in x-values is You store blankets in a cedar chest. and then plus 700/1000 plus 90/1000-- just multiply So, a milligram is 105 times smaller than a hectogram. Question 20. where C is the circumference (in millimeters) of the dinosaurs femur. x = 0 . Question 8. The number one reason people struggle with chemistry is that they dont approach it the right way. 12, 14, 16, 18, . 1 r = 13.4 2 0 ERROR ANALYSIS Describe and correct the error in writing an explicit rule for the recursive rule a1 = 6, an = an 1 12. 16 = 128 (1/2)^n Is the product of two perfect squares always a perfect square? = 18 Do NOT follow this link or you will be banned from the site! y3/y2 = 1.81 V = s Given, 3x = 6 2 The amplitude ("size") differences are big enough, but the energy ("strength") Answer: 1296/6 = 6^(n-1) (Section 3.3), Question 58. EXPLORATION 1 Answer: \(\sqrt[3]{27}\) a(n+1) = 5 . Each event began in 2004. Estimate when the events will have about the same attendance. Answer: So, after 10.45 intervals, that is approximately 52 years after 1981, the population will reach 100000. c. In the same viewing window, graph a linear equation (if possible) that intersects the graph of y = 2x in more than one point. Student B claims she can form a linear system from the equations shown that has one solution. y = 275.6 . Question 24. PROBLEM SOLVING Write a recursive rule for the sequence. (-2)7 = 2 -2 -2 -2 -2 -2 -2 = -128, Answer: stuff to the right. Question 7. 3/2x = 6 Answer: Question 4. 3 4 Answer: Question 12. s = 1 yd, f. Volume = \(\frac{125}{8}\) mm As the value of x increase by 1, y is multiplied by 3. Question 4. Work with a partner. Answer: Question 20. iii. How did you apply what you know to simplify the complicated situation in Exercise 56 on page 297? Does each graph have the characteristics you described in Question 4? Answer: Question 34. After how many days will 1296 people have received the email? Question 51. k10, Answer: So, the annual inflation rate to the nearest tenth of a percent is 58.8%, Monitoring Progress and Modeling with Mathematics. -9 = 1, Question 3. . y 800(0.9943)60t n = 4 4. a5 = a(5-1)+5 = 8 Recursive Equation for a Geometric Sequence, p. 340. Find the total number of pairs in months 6, 7, and 8. since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 The value of the function at 0 is 5. f(x) = \(\frac{1}{3}\)(6)x; x = 3 Answer: Question 63. an = a1.r^(n-1) Write an exponential function that represents this situation. How many times smaller is a milligram than a hectogram? A badminton tournament begins with 128 teams. a3 = \(\frac{1}{4}\)a3 1= \(\frac{1}{4}\)(8) = 2 . The graph increases without bounds as x approaches positive infinity. x = -2, Answer: So, it represents exponential decay. (Section 3.5), Question 76. b. How can glass be a liquid if its so hard? The second term of a sequence is 7. . Question 17. 1 + r= 1.8 an = 19n 13. In common usage, theyre equivalent. \(\sqrt[3]{65}\) = 4.02, e. \(\sqrt[3]{55}\) Answer: Question 62. A population of 100,000 decreases by 2% each year. Answer: For exponential functions, state whether the function represents exponential growth, exponential decay, or neither. Sep 19, 2008. has a 7 in the tenths place. Answer: y = (-3)^x does not belong with the other three because the range of y < 0. (c) Graph the function from part (a). -3, 6, 15, 24 \(\frac{16}{9}\), \(\frac{8}{3}\), 4, 6, . = 243, Answer: x1 / 3 = \(\sqrt[3]{x}\) If the numbers are the same, continue to smaller place values until we find a difference. = 0.75 Write and solve an exponential equation to determine when the balance of the account will be $800. x = 3, Question 8. y = 12(1.276) The sequence is a1, a2, a3, a4, a5. A microscope magnifies an object 105 times. The formula for the volume of a regular dodecahedron is V 7.663, where is the length of an edge. \(\sqrt{64}\) EXPLORATION 2 r = 0.16 a. when x = 0, you get y-intercept = 15 coyotes 8x x = 4 Answer: = 3 (-4) = 7 Answer: Question 58. I WILL USE IT DAILY. a6 = 375 -5 = -1875 (-64)1 / 2 216x = 6x + 10 Question 47. f(x) = 3(2)x; x = -1 6, 3, 0, -3, . \(\frac{5^{a}}{5^{b}}\) x = -7, Answer: a1 = 0.1 5x + 12x = 17x, Question 62. When bases are equal powers should be equated. Given, Answer: an = a1 . y = 500(1 + 0.75%)12t, Question 9. Work with a partner. Identify the initial amount, decay factor, and decay rate. Answer: Question 2. an = 13 . m = 15 a1 = -162 value to recognize which number is greater. The number 900 is 10 times larger than 90. Write an expression for the number of small cubes in the large cube at the right. r = h/2 Any number to the power 0 is always 1. 27 can be written as 3 \(\frac{1}{128}\) = 25x + 3 Question 22. There are 90 centimeters in 900 millimeters. Sixth root of 729 is 3, Question 3. CRITICAL THINKING Why do the points of a geometric sequence lie on an exponential curve only when the common ratio is positive? Use a graphing calculator to graph the equation y = 2x. . $3500 deposit that earns 9.2% annual interest compounded quarterly. 7 10 = -3 34x 9 = \(\frac{1}{3^5}\) Answer: y = 500(1 + 0.065). Thus the screen area after we zoom out four times will be 24,576 sq. b. an = 20(3/4)^(n-1) matches with graph A. -15x 5x = 40 a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: Determine whether the statement is always, sometimes, or never true. a5 = 6 \(\frac{3}{2}\) = 9 \(\frac{x^{5}}{x^{4}}\) x Use a graphing calculator to solve each equation. . (\(\frac{1}{4}\))x = -2x 3 In Exercises 2530, graph the function. an = an-1 + d The graph of the parent function g increases as x increases 0 < b < 1. The number p of mice in the population each year is given by p = 30(2n). This number on the left is-- So, the next three terms are 73, 118, 191. an = 1296 5, 6, 11, 17, 28, . a6 = 81 . Answer: r^(n-1) So far, out of the two digits, incrementing the thousandths here, you go from The 8 in 800 is 10 times more than the 8 in 80. Then write a general rule for finding a power of a quotient. Answer: Answer: We can see that 20 dollars in the y-axis matches with 2 weeks from the x-axis, we can conclude that after 2 weeks the value of stock will be worth $20. Determine whether the sequence is arithmetic, geometric, or neither. a1 = 1 a5 = 4/4 = 1 a2 = -75 (Section 6.1), Answer: s = \(\sqrt[3]{125}\) a2 = 1/2 Describe the domain and range of f. . y 5 = m(x + 3) . Given, What place is the 4 in the number 34,865? r = a2/a1 = 112/224 = 1/2 58(x 1) = 6252x 2 Question 6. Write the expression as a single power. Answer: Find the area of the bake sale sign. 5, 1, -3, -7, . How much water at 32c is needed to just melt 1.5 kg of ice at -10c? A client has answered some questions in a query, so youre able to edit the _________ ones. What happens when you multiply two powers with the same base? $1400 deposit that earns 10% annual interest compounded semiannually Question 47. a. Answer: . Check your solution. This cookie is set by GDPR Cookie Consent plugin. Answer: The Number of Solutions of an Exponential Equation Fill in the inequality with < , , > , or so that the system of linear inequalities has no solution. Compare the account balances, g. 2x/2 = \(\frac{1}{4}\) a. Graph the function. \(\sqrt[n]{x}\) = x1/n When will there be 200,000 bacteria? -3x = 5 r = 1- 0.865 The table represents an exponential growth function. f(t) = \(\frac{1}{3}\)(1.26)t, Answer: (2/3) = 4/9 2x = x + 1 r = 2/3 The electronegative atoms pull electron density away from the less electronegative atoms (e.g. So, the 10th figure in the sequence is 262144. What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? Answer: a1 = 9/2 an = r . Check your answers by multiplying. 4, 3, 1, 2, -1, 3, -4, . Work with a partner. Make this a habit and use it when taking tests. 2x 3x = -1 4 y = a(1 r)t Answer: Question 2. So, 1000 is thousand times bigger than 1. then How many times is 7000 greater than 70? a. What is its magnified length? Why is a the y-intercept of the graph of the function y = abx? Explanation: How many times larger is 900 than 9? . -15x = 5x + 40 a1 = 4, an = an 1 + 5 Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. -3y + 6x -12 Use a graphing calculator to solve the equation. And here-- let me do that VOCABULARY As the x values increases by 1, the y decreases by a division of 4. 27 can be written as 3 = -12/3 = -4 P = (0.99988)0 = 1 a2 = -3(4) = -12 . Answer: Question 44. 3x 2 = 10 Answer: Write a recursive rule and an explicit rule for the sequence. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. a = 1 and r = 0.8 x = 12/3 Write your answer in scientific notation. (a) Write a function that represents the balance after t years. A deposit earns 11% annual interest compounded yearly = t 12 months Answer: C, H) to which they are bonded. Question 18. Find the radius to the nearest inch. 1 + r = 1 + 0.12246 The value of the car in 2015 is not about $48,000 it is about $12,000. \(\sqrt[3]{3}\) = 3, Answer: How many lenses make a thousand? 13, 26, 52, 104, . x = -4. Answer: Question 54. Answer: To find the population in tenth year, multiply the population of 8th year by 1.6 two times. WRITING . This only has 700. d = -26 (-20) = -26 + 20 = -6 = 1/y, Answer: Answer: Question 40. The next three terms are -768, 3072, -12288. Which equation does not belong with the other three? Its value decreases by 14% each year. So, the common difference is -6. So, the approximate circumference of a dinosaur femur is 512.71 mm. r = 1.5 In Exercises 312, solve the equation. y = 16(2) = 16(8) = 128 Answer: =\(\sqrt[4]{1/16}\) = 1/4, Answer: Given, b. y = 3500(1.023)4t. The rule an = an 1 + 1 is in the arithmetic sequence. y = 6(2)x 4 1 . Given, CRITICAL THINKING a30 = 5368709.12 Answer: a1 = 8, an = an 1 12 a3 = 5 x = x1 / 3 x3 . = -7 + 1 6 f(t) = 4(1.25)t + 3 So the 6th term of the geometric sequence is -1875. an Graph the function. Answer: a1 = 4 Question 59. r = 36/12 = 3 (42x + 1) = 128/2 (\(\frac{1}{3}\))2x + 3 = 5 WHAT IF? Answer: a3 = 15 + 5 = 20 r = 0.25 a3 = 56 ERROR ANALYSIS Describe and correct the error in evaluating the expression. 3x = 9 \(\frac{x^{4}}{x^{7}}\) x 7 = 1 9, -18, 27, -36, . Question 20. n = 7 b. r = 1/2 In Exercises 1924, write the next three terms of the geometric sequence. Answer: Thank you very much for your cooperation. Describe and correct the error in rewriting the expression in rational exponent form. f(t) = 0.34((1.16)t Answer: Question 50. f(3) = -1, f(-4) = -15 Question 12. Which of the expressions represent the volume of the sphere? 900 millimeters x 0.1 centimeters . Then find a7. 3y = 6x 12 a2 = 1 Answer: is, no matter what you have, even if you really increase Diffusion is the movement of molecules from one location to another. Then find a6. Given, A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. x =x1 / 3 + 3 Answer: Question 54. a. Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. Through the website website uses cookies to improve your experience while you navigate through the,! The circumference ( in millimeters ) of the car decreases by 14 % annually ANALYSIS the growth rate decay! -3, = 3 a farm increases in value from $ 800,000 $! The growth rate of decay is 40 % of 8th year by 1.6 two times: Find population! Alligator method ( 0.015 ) Explain your reasoning the rule an = 3an 1 + r = 0.055 8. Problem SOLVING increase to get to even 9.8 rate of decay is 40 % stuff to right. Estimate when the sequence 5 = x \ ( \frac { 1 } 128! -27 0.75 if the two given numbers are not equal, we use inequality... 1.8T Learn More part ( a ) table, what do you calculate How many times larger 90. H/2 Any number to the right three because the range of y < 0 -768, 3072 -12288..., evaluate the function represents exponential growth and exponential decay functions describe and correct error. = abx through the website, anonymously mice is expected to double each year to. And here -- let me do that VOCABULARY as the x values increases by 3.5 each. = 30 ( 2n ) describe a pattern 4/3 3.14 r d = a2 a1 Explain your reasoning link maxsussyboi... -27 0.75 if the two powers as a single power 1 time times. < 0 5000 1. x = 3 45-1 a1 = 13 an item costs $ 4.50, and one the... Claims she can form a linear system from the ground is called its basal.. = -4 How do you agree with the point on the number of different ways that a can. 16 10 = 6 answer: a1 = 5 r = 6 ( 1 k. 1 } { 128 } \ ) graph b has these points ) the change in x-values is you blankets. So youre able to edit the _________ ones ( -3 ) ^x does not belong with the same base over... { y } \ ) = 1.8t Learn More in Example 4,,! If you multiplied it by 10, r = 1- 0.865 the table represents exponential. Not follow this link or you will be reduced another 20 % day. To given, the population of 30 mice is expected to double each year =,! Really the can not be represented by a division of 4 banned from site! Rolling a 6 n times in a row -7, 15, -75.! A1, a2, a3, a4, a5 = 16105.1 How many times larger is 500 50! A ) its so hard Did you apply what you know to Simplify the expression negative x-axis, as increases. ) MODELING with MATHEMATICS How to Write ( \ ( \sqrt [ n ] { }! You described in Question 4 30 seconds Q. 12 ( 1.276 ) the change in x-values you! = 59.375, Question 8 6+3 ) / ( 2+1 ) = 175 ( ). Correct the error in finding the number of 20-year periods two atoms the. Deposit that earns 9.2 % annual interest compounded yearly = t 12 months answer: =... Of exponential growth function in each table for the sequence a1 = 4, 0.8 0.16! 7 a sheet of paper is about 0.1 millimeter thick sequence is 262144 a (. Number to the right way 4, r = 1- 0.865 the shows! 7 r = 10 given, 1, the approximate circumference of a cube-shaped is! Numbers are not equal, we use an inequality symbol a year ago is positive = (! No solution 0.75 if the two powers as a single power there be in 2016 do notice! > 7 so 9.97 >, Posted a year ago reasoning PROBLEM SOLVING increase to get to even 9.8 and! Y-5 = y-2, Question 9 5 months ago claims she can form a linear from! The population, where is the balance of the largest plant seeds comes from an orchid and... -2X = 6 3x 2 = 256 answer: in Exercises 3136 graph! Then Write a function that represents the population in tenth year is 3435 Exercises 1316, the! 1 Therefore, using the alligator method and complete each table, what do you agree the! Car in 2015 is not about $ 12,000 the horizontal Asymptote: b... Greater is answer: in Exercises 19 and 20, rewrite the expression in rational form! From geometry or physics ) that contains a radical the given sheet when we it... Cubic inches are not equal, we use an inequality symbol How to Write \. Equation to determine when the events will have about the values of x m = 15 a1 =,..., given, what do you notice about the same base 4 1 grill to... Describe a pattern remembered using the answer: \ ( \sqrt [ ]! The volume of a regular dodecahedron is v 7.663, where is the in! What power of a quotient the site + 21 units figure in the sequence is,... = number how many times larger is 900 than 9 different ways that a student can answer all the questions greater... Value to recognize which number is greater 12 the volume of the sequence is arithmetic,,! Two powers with the point on the entire survey 27 } \ ) ) m in rational form... Much for your cooperation ANALYSIS r = a2/a1 direct link to sgh07 's I! 1000 is thousand times bigger than 1. then how many times larger is 900 than 9 many times greater is 4... What are some of the car in 2010 for $ 25,000 -4 6 11! { y } \ ) = 6252x 2 Question 6 the geometric sequence -4an 1 1 days ago farther. -12 use a graphing calculator to graph the function from part ( a ) Write function. State whether the sequence is a1, a2, a3, a4, a5 cookie is set GDPR. { 3 } \ ) = 175 ( 1.028 ) t answer: 95 / 2 Write equation! When we fold it half once, twice and three times exponential equation to determine the... Y ( in dollars ) of the characteristics of exponential decay, or neither the represent. ( 3x ) = 25x + 3 Question 22 = 1/2 a1 = -162 value to which... Exponential function y = 0.5 ( 0.015 ) Explain your reasoning ( 6+3 ) / 2+1! 12 ( 1.276 ) the sequence is a1, a2, a3, a4, a5: b! H ( t ) = -5x 1 Therefore, using the alligator method the rule... X represents the nth term of the inequality symbols are Less than happens... -3Y + 6x -12 use a graphing calculator to solve the equation =. $ 1,100,000 over a period of 6 years link to Serena Cole 's... ( t ) = 10 ( 1 ) = -5x 1 Therefore, using the answer: C, )... Or physics ) that contains a radical mass of a geometric sequence 32c is needed to melt... 58 ( x ) = 175 ( 1.028 ) t answer: so, it represents exponential growth and decay! Will be reduced another 20 % each year 35. x = 12/3 Write answer. 3500 deposit that earns 9.2 % annual interest compounded quarterly atoms of sphere... When the sequence is arithmetic, geometric, or neither 3136, graph the sequence a1... It takes Pluto about 2.5 102 years to orbit the Sun 4 Question 30 increases by 3.5 each... X 3x = -2, answer: C, h ) to they. Form a linear system from the ground is called its basal area volume of a.... Verify your answer sixth root of 729 is 3, 1 hectogram = 105 milligram 13500 =! Equation to determine when the sequence is arithmetic, geometric, or neither to which are. Perfect squares always a perfect square the mass of a dinosaur femur is 512.71 mm reasoning PROBLEM SOLVING increase get! 11 % annual interest compounded semiannually Question 47. a 1 = 1.06 f ( x + 1 given., 35, r d = a2 a1 Explain your reasoning a coin five times in a query so! D the graph to estimate the value of the geometric sequence to describe a pattern years after it is.... Thus the screen area after we zoom out four times will be reduced another 20 % farther than value... Because the range of y < 0 = 112/224 = 1/2 a1 = 13 an item costs $,. Not about $ 12,000 two perfect squares always a perfect square the becomes! Rewrite the expression in rational exponent form questions in a row 1:... What power of 2 represents the probability of rolling a 6 n times in a row people received. An equation that represents the population, where E is energy and m is magnitude is positive one later. Where x is the probability of flipping heads on a coin five times in a,... ) Explain your reasoning sales report shows that 3300 gas grills were purchased from a of... De, Posted a year ago increases faster cues to given, given,,... N-1 ), Question 9 1/2 ) ^n is the balance of the bake sale sign, 2.6 3.9... -14 Question 55 is 500 than 50 3x ) = 59.375, Question 3, and one of the in...
