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Exponential Function Solving - Growth (Discrete) Scenario to Value at Time

Level 1

This math topic covers the application of exponential functions to solve real-world scenarios involving growth. It focuses on computing the future value of populations, account balances, or debt, applying the formula for exponential growth given initial values and constant growth rates over discrete time intervals. The problems cater to the calculation of rabbit population growth, savings account interest accumulation, and credit card debt increase. Each question involves determining the final value after a specified number of time periods with given annual or monthly growth rates.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solving - Growth (Discrete) Scenario to Value at Time Worksheet

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Exponential Function Solving - Growth (Discrete) Scenario to Value at...
1
A rabbit population starts at 900. Each subsequent yearly breeding season it grows by 4%. After 6 years it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing 4 + P = P sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 4 + P = P sub 0 over (1 + r) to the power of ( t)
2
A rabbit population starts at 200. Each subsequent yearly breeding season it grows by 8%. After 7 years it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 3 + P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 0 + P = P sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 9 + P = P sub 0 over (1 + r) to the power of ( t)
3
A savings account starts with $600. Each subsequent month it earns 3% in interest. After 2 months it has a certain amount of cash.
Solve for the final cash given this scenario?
a A LaTex expression showing 1 + P = P sub 0 over (1 + r) to the power of ( t)
b A LaTex expression showing 3 + P = P sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 4 + P = P sub 0 times (1 - r) to the power of ( t)
d A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
4
A savings account starts with $500. Each subsequent quarter it earns 3% in interest. After 2 quarters it has a certain amount of cash.
Solve for the final cash given this scenario?
a A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing 9 + P = P sub 0 over (1 + r) to the power of ( t)
c A LaTex expression showing 5 + P = P sub 0 times (1 - r) to the power of ( t)
d A LaTex expression showing 1 + P = P sub 0 times (1 - r) to the power of ( t)
5
A credit card starts with $500 of debt. Each subsequent month it grows by 3% in interest. After 4 months the debt has grown to a certain amount.
Solve for the final debt given this scenario?
a A LaTex expression showing 5 + D = D sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 8 + D = D sub 0 over (1 + r) to the power of ( t)
c A LaTex expression showing D = D sub 0 times (1 + r) to the power of ( t)
6
A rabbit population starts at 400. Each subsequent yearly breeding season it grows by 7%. After 3 years it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing 8 + P = P sub 0 over (1 + r) to the power of ( t)
c A LaTex expression showing 2 + P = P sub 0 over (1 + r) to the power of ( t)
7
A rabbit population starts at 200. Each subsequent yearly breeding season it grows by 9%. After 7 years it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 1 + P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing P = P sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 5 + P = P sub 0 over (1 + r) to the power of ( t)
d A LaTex expression showing 8 + P = P sub 0 times (1 - r) to the power of ( t)
8
A credit card starts with $800 of debt. Each subsequent year it grows by 3% in interest. After 9 years the debt has grown to a certain amount.
Solve for the final debt given this scenario?
a A LaTex expression showing 5 + D = D sub 0 over (1 + r) to the power of ( t)
b A LaTex expression showing D = D sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 9 + D = D sub 0 times (1 - r) to the power of ( t)
d A LaTex expression showing 9 + D = D sub 0 over (1 + r) to the power of ( t)