Exponential Growth & Decay - NJCTLcontent.njctl.org/courses/math/algebra-ii/numbers-and...2015/11/19 · Algebra II – Exponential Growth & Decay ~2~ NJCTL.org PARCC-type Questions:

Algebra II – Exponential Growth & Decay ~1~ NJCTL.org

Exponential Growth & Decay

Simple Annual Interest Classwork 1) What will be your bank balance if you put $700 in your account and earn 4% simple annual interest

for eight years? 2) What will be your bank balance if you put $950 in your account and earn 6% simple annual interest

for eleven years? 3) What will be your bank balance if you put $1,025 in your account and earn 5.5% simple annual

interest for nine years? 4) If you are earning 6.5% simple annual interest and your goal is to have $4,500 in your account after

twelve years, how much will you have to initially deposit? 5) If you are earning 3.5% simple annual interest and your goal is to have $1,250 in your account after

five years, how much will you have to initially deposit? 6) If you are earning 5.75% simple annual interest and your goal is to have $2,750 in your account after

ten years, how much will you have to initially deposit? Simple Annual Interest Homework 7) What will be your bank balance if you put $650 in your account and earn 5% simple annual interest

for six years? 8) What will be your bank balance if you put $1,300 in your account and earn 8% simple annual interest

for ten years? 9) What will be your bank balance if you put $1,425 in your account and earn 6.5% simple annual

interest for thirteen years? 10) If you are earning 7% simple annual interest and your goal is to have $3,500 in your account after ten

years, how much will you have to initially deposit? 11) If you are earning 4.5% simple annual interest and your goal is to have $1,450 in your account after

seven years, how much will you have to initially deposit? 12) If you are earning 6.25% simple annual interest and your goal is to have $2,250 in your account after

eleven years, how much will you have to initially deposit? Compound Interest Classwork 13) What will be your bank balance if you put $850 in your account and earn 5.5% interest, compounded

monthly, for eight years? 14) What will be your bank balance if you put $1,725 in your account and earn 4% interest, compounded

weekly, for ten years? 15) What will be your bank balance if you put $920 in your account and earn 6.5% interest, compounded

daily, for nine years?


PARCC-type Questions: 16) If you are earning 6% interest, compounded monthly, and your goal is to have $2,225 in your account

after four years, how much will you have to initially deposit? 17) If you are earning 4.25% interest, compounded quarterly, and your goal is to have $2,750 in your

account after seven years, how much will you have to initially deposit? 18) If you are earning 4.75% interest, compounded weekly, and your goal is to have $5,350 in your

account after twelve years, how much will you have to initially deposit? 19) How much was originally invested if you have $2,954.69 in an account generating 4.5% interest,

compounded monthly over 14 years? 20) How much was originally invested if you have $6,593.31 in an account generating 6.5% interest,

compounded quarterly over 16 years? 21) What interest rate is needed to double your money if it’s invested for 11 years, compounded weekly? 22) What interest rate is needed to triple your money if it’s invested for 25 years, compounded daily? Compound Interest Homework 23) What will be your bank balance if you put $525 in your account and earn 4% interest, compounded

quarterly, for six years? 24) What will be your bank balance if you put $1,550 in your account and earn 8.75% interest,

compounded daily, for ten years? 25) What will be your bank balance if you put $1,775 in your account and earn 7.5% interest,

compounded weekly, for six years? PARCC-type Questions: 26) If you are earning 6% interest, compounded daily, and your goal is to have $4,800 in your account

after thirteen years, how much will you have to initially deposit? 27) If you are earning 4.25% interest, compounded quarterly, and your goal is to have $1,975 in your

account after eight years, how much will you have to initially deposit? 28) If you are earning 6.75% interest, compounded monthly, and your goal is to have $4,000 in your

account after twelve years, how much will you have to initially deposit? 29) How much was originally invested if you have $3,701.07 in an account generating 5.5% interest,

compounded monthly, over 15 years? 30) How much was originally invested if you have $6,475.03 in an account generating 6.25% interest,

compounded quarterly, over 18 years? 31) What interest rate is needed to double your money if it’s invested for 10 years, compounded

quarterly? 32) What interest rate is needed to triple your money if it’s invested for 30 years, compounded monthly?


The Constant, e Classwork 33) What will be your bank balance if you put $1,700 in your account and earn 5% interest, compounded

continuously, for nine years? 34) What will be your bank balance if you put $250 in your account and earn 6.5% interest, compounded

continuously, for fifteen years? 35) What will be your bank balance if you put $725 in your account and earn 4.5% interest, compounded

continuously, for ten years? PARCC-type Questions: 36) If you are earning 8% interest, compounded continuously, and your goal is to have $4,000 in your

account after eleven years, how much will you have to initially deposit? 37) If you are earning 6.35% interest, compounded continuously, and your goal is to have $2,240 in your

account after eight years, how much will you have to initially deposit? 38) If you are earning 4.75% interest, compounded continuously, and your goal is to have $3,775 in your

account after nine years, how much will you have to initially deposit? The Constant, e Homework 39) What will be your bank balance if you put $525 in your account and earn 5.8% interest, compounded

continuously, for seven years? 40) What will be your bank balance if you put $1,200 in your account and earn 8.25% interest,

compounded continuously, for twenty years? 41) What will be your bank balance if you put $1,365 in your account and earn 5.5% interest,

compounded continuously, for three years? PARCC-type Questions: 42) If you are earning 6.3% interest, compounded continuously, and your goal is to have $2,200 in your

account after twelve years, how much will you have to initially deposit? 43) If you are earning 4.75% interest, compounded continuously, and your goal is to have $1,520 in your

account after six years, how much will you have to initially deposit? 44) If you are earning 6.9% interest, compounded continuously, and your goal is to have $2,530 in your

account after seven years, how much will you have to initially deposit? Population Growth Classwork 45) A town’s population is growing at a rate of 2.4% per year. If its initial population is 1.3 million people,

what will be its population in 9 years?


46) The 2010 census showed the population in Kansas to be 2.853 million people. If the population

grows at 1.8%, how many people will live in Kansas in 2018? 47) The 2010 census showed the population in Pennsylvania to be 12.7 million people. If the population

grows at 0.7%, how many people will live in Pennsylvania in 2019? 48) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.075)𝑡.

a) At what percentage rate is the population growing?

b) If the initial population is 3.2 million, what will the population be after 2 years?

c) If the initial population is 2.8 million, what will the population be after 5 years?

49) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.092)𝑡.




PARCC-type Questions: 50) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.08)𝑡.


b) If the initial population is 2.4 million, what will the population be after 3 months?

c) If the initial population is 2.4 million, what will the population be after 17 months?









Population Growth Homework 53) A town’s population is growing at a rate of 0.9% per year. If its initial population is 1.1 million people,

what will be its population in 12 years?


54) The 2010 census showed the population in New York to be 19.378 million people. If the population

grows at 1.9%, how many people will live in New York in 2017? 55) The 2010 census showed the population in New Jersey to be 8.792 million people. If the population

grows at 1.7%, how many people will live in New Jersey in 2020? 56) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.023)𝑡.








PARCC-type Questions: 58) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.035)𝑡.












Half-Lives and Decay Applications Classwork

61) If the half-life of a substance was 16 days, and only 1

8 of it remains, how many days have elapsed?




63) After 240 days, how many grams will remain of a 150-gram sample if the half-life for that substance is

60 days? 64) After 1 year, how many grams will remain of a 170-gram sample if the half-life for that substance is 80

days? Assume that it is not a leap year. 65) A certain radioactive material has a half-life of 22 years. If 200 grams were present to start, how

much will remain in 32 years? 66) A certain radioactive material has a half-life of 17 years. If 250 grams were present to start, how

much will remain in 55 years? 67) A new car depreciates at a rate of 8.5% per year. If you purchase it for $28,000, how much is it worth

after 8 years? 68) A new SUV depreciates at a rate of 9.5% per year. If you purchase one for $43,250, how much is it

worth after 12 years? 69) A new sofa depreciates at a rate of 21% per year. If a 6-year old sofa is worth $450, how much was it

originally worth? PARCC-type Questions 70) The population of a city has been decreasing at a rate of 6.5% per year.

a) If its population after 12 years is 500,367, what was the initial population?

b) What was the city’s population after 7 years?

c) What was the city’s population after 19 months? 71) When approximating the age of an artifact that is less than 50,000 years old, the radioisotope carbon-

14 can be used. Carbon-14 is an element with the property that every 5,730 years, the mass of the element in a sample is reduced by half. The mass of the carbon-14 artifact can be modeled by an exponential function, m, of its age, x. Part A Let A represent the original mass of carbon-14. Which function is an appropriate model?

a) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥

b) 𝑚(𝑥) = 𝐴 ∙ 2−𝑥

5,730

c) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥

50,000

d) 𝑚(𝑥) = 𝐴 ∙ 2−50,000𝑥

5,730 Part B Based on the situation, which interval represents the domain of the function, m? a) 0 ≤ 𝑥 ≤ 50,000

b) 0 ≤ 𝑥 ≤ 5,730

c) −∞ < 𝑥 < ∞ d) 0 ≤ 𝑥 < ∞ Part C Which statements describe the graph of m in the coordinate plane? Select all that apply. a) The function m is a periodic function. b) The function m is a decreasing function.


c) The function m is an increasing function. d) The function m is a nonlinear function. e) The function m is a linear function. Part D At what age would the mass of carbon-14 in an artifact be one-eighth of the original amount? a) 716.25 years old b) 2,865 years old c) 11,460 years old d) 17,190 years old

Half-Lives and Decay Applications Homework






30 days? 75) After 1 year, how many grams will remain of a 220-gram sample if the half-life for that substance is 70

days? Assume that it is not a leap year. 76) A certain radioactive material has a half-life of 29 years. If 330 grams were present to start, how

much will remain in 27 years? 77) A certain radioactive material has a half-life of 19 years. If 280 grams were present to start, how

much will remain in 57 years? 78) A new car depreciates at a rate of 8% per year. If you purchase it for $30,000, how much is it worth

after 6 years? 79) A new SUV depreciates at a rate of 9.5% per year. If you purchase one for $44,725, how much is it

worth after 11 years? 80) A new sofa depreciates at a rate of 22% per year. If a 7-year old sofa is worth $475, how much was it

originally worth? PARCC-type Questions 81) The population of a city has been decreasing at a rate of 5.25% per year.

a) If its population after 9 years is 450,645, what was the initial population?


c) What was the city’s population after 9 months? 82) When approximating the age of an artifact that is less than 60,000 years old, the radioisotope carbon-



a) 𝑚(𝑥) = 𝐴 ∙ 2−60,000𝑥

5,730

b) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥

60,000

c) 𝑚(𝑥) = 𝐴 ∙ 2−𝑥

5,730

d) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥 Part B Based on the situation, which interval represents the domain of the function, m? a) 0 ≤ 𝑥 < ∞

b) 0 ≤ 𝑥 ≤ 60,000

c) 0 ≤ 𝑥 ≤ 5,730 d) −∞ < 𝑥 < ∞ Part C Which statements describe the graph of m in the coordinate plane? Select all that apply. a) The function m is an increasing function. b) The function m is a decreasing function. c) The function m is a periodic function. d) The function m is a linear function. e) The function m is a nonlinear function. Part D At what age would the mass of carbon-14 in an artifact be one-sixteenth of the original amount? a) 358.125 years old b) 11,460 years old c) 17,190 years old d) 22,920 years old


Chapter Review

1) What will be your bank balance if you put $1,300 in your account and earn 5% simple annual interest for twelve years?

2) What will be your bank balance if you put $3,750 in your account and earn 4.5% interest,

compounded monthly, for ten years? 3) What will be your bank balance if you put $2,400 in your account and earn 5.25% interest,

compounded continuously, for sixteen years? 4) If you are earning 7.5% interest, compounded annually, and your goal is to have $4,750 in your

account after fifteen years, how much will you have to initially deposit? 5) If you are earning 6.25% interest, compounded weekly, and your goal is to have $2,750 in your

account after six years, how much will you have to initially deposit? 6) If you are earning 5.75% interest, compounded quarterly, and your goal is to have $3,250 in your

account after eight years, how much will you have to initially deposit? 7) If you are earning 8% interest, compounded continuously, and your goal is to have $4,000 in your

account after eleven years, how much will you have to initially deposit? 8) The 2010 census showed the population in Nebraska to be 1.826 million people. If the population

grows at 3%, how many people will live in Nebraska in 2021? 9) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.087)𝑡.



c) If the initial population is 3.25 million, what will the population be after 9 years? 10) The annual population of a city can be modeled by the equation 𝐴 = 𝑃(1.125)𝑡.




11) If the half-life of the substance was 12 days, and only 1



50 days? 13) A certain radioactive material has a half-life of 15 years. If 250 grams were present to start, how

much will remain in 42 years? 14) A new car depreciates at a rate of 8% per year. If you purchase it for $25,000, how much is it worth

after 9 years? 15) A new truck depreciates at a rate of 8.5% per year. If a 7-year old truck is worth $17,642, how much

was it originally worth?


16) The population of a city has been decreasing at a rate of 7.35% per year. a) If its population after 15 years is 512,984, what was the initial population?


c) What was the city’s population after 29 months?

17) When approximating the age of an artifact that is less than 30,000 years old, the radioisotope carbon-


a) 𝑚(𝑥) = 𝐴 ∙ 2−𝑥

5,730

b) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥

c) 𝑚(𝑥) = 𝐴 ∙ 2−30,000𝑥

5,730

d) 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥

30,000 Part B Based on the situation, which interval represents the domain of the function, m? a) −∞ < 𝑥 < ∞

b) 0 ≤ 𝑥 < ∞ c) 0 ≤ 𝑥 ≤ 5,730

d) 0 ≤ 𝑥 ≤ 30,000 Part C Which statements describe the graph of m in the coordinate plane? Select all that apply. a) The function m is a periodic function. b) The function m is a linear function. c) The function m is a nonlinear function. d) The function m is an increasing function. e) The function m is a decreasing function. Part D At what age would the mass of carbon-14 in an artifact be one-fourth of the original amount? a) 22,920 years old b) 11,460 years old c) 2,865 years old d) 1,432.5 years old


Answer Key

1. $924.00 2. $1,577.00 3. $1,532.38 4. $2,528.09 5. $1,063.83 6. $1,746.03 7. $845.00 8. $2,340.00 9. $2,629.13 10. $2,058.82 11. $1,102.66 12. $1,333.33 13. $1,318.48 14. $2573.00 15. $1,651.31 16. $1,751.29 17. $2,045.56 18. $3,026.35 19. $1,575.50 20. $2,350.00 21. r = 6.31% 22. r = 4.39% 23. $666.61 24. $3,717.87 25. $2,782.85 26. $2,200.49 27. $1,408.27 28. $1,783.48 29. $1,625.00 30. $2,120.50 31. r = 6.99% 32. r = 3.67% 33. $2,666.13 34. $662.79 35. $1,137.03 36. $1,659.13 37. $1,347.80 38. $2,461.82 39. $787.92 40. $6,248.38 41. $1,609.87 42. $1,032.99 43. $1,143.06 44. $1,560.83 45. 1.609 million people 46. 3.291 million people 47. 13.523 million people 48.

a. 7.5% b. 3.698 million people c. 4.020 million people

49. a. 9.2% b. 4.558 million people

c. 5.370 million people 50.

a. 8% b. 2.447 million people c. 2.676 million people

51. a. 17% b. 2.082 million people c. 2.534 million people

52. a. 6.5% b. 1.147 million people c. 1.254 million people

53. 1.225 million people 54. 22.107 million people 55. 10.406 million people 56.

a. 2.3% b. 3.395 million people c. 3.375 million people



59. a. 12% b. 2.593 million people c. 3.132 million people


61. 48 days 62. 168 days 63. 9.375 grams 64. 7.194 grams 65. 72.974 grams 66. 26.547 grams 67. $13,757.10 68. $13,054.77 69. $1,851.19 70.

a. 1,120,855 people b. 700,214 people c. 1,007,707 people

71. Part A: b Part B: a Part C: b and d Part D: d

72. 120 days


73. 238 days 74. 0.293 grams 75. 5.926 grams 76. 173.079 grams 77. 35 grams 78. $18,190.65 79. $14,917.11 80. $2,704.15 81.

a. 732,186 people b. 383,329 people c. 703,163 people

82. Part A: c Part B: b Part C: b and e Part D: d

Review: 1) $2,080.00 2) $5,876.22 3) $5,559.28 4) $1,605.34 5) $1,890.47 6) $2,058.40 7) $1,659.13 8) 2.528 million people 9)

a) 8.7% b) 2.234 million people c) 6.886 million people

10) a) 12.5% b) 3.571 million people c) 4.178 million people

11) 48 days 12) 1.25 grams 13) 35.897 grams 14) $11,804.03 15) $32,854.90 16)

a) 1,612,213 people b) 1,019,753 people c) 1,340,599 people

17) Part A: a Part B: d Part C: c and e Part D: b

Exponential Growth & Decay - NJCTLcontent.njctl.org/courses/math/algebra-ii/numbers-and...2015/11/19 · Algebra II – Exponential Growth & Decay ~2~ NJCTL.org PARCC-type Questions:

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