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Exponential Function Solving - Growth (Discrete) Scenario to Rate

Level 1

This topic covers solving for the growth rate in exponential function scenarios involving discrete time periods, specifically focusing on situations where populations or amounts grow by a certain percent each period. Problems require calculating the rate of increase over a set number of years given initial and final amounts, using exponential growth formulas. This skill is essential for understanding real-world exponential growth situations such as population dynamics or financial investments. Each problem offers multiple-choice answers, presenting various exponential equation forms to discern the correct growth rate.

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 Rate Worksheet

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Exponential Function Solving - Growth (Discrete) Scenario to Rate
1
An insect population starts at 300. Each subsequent yearly breeding season it grows by a certain percent. After 6 years it has increased to a population of 450.
Solve for the rate given this scenario?
a A LaTex expression showing 4 + r = +(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 7 + r = +(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 9 + r = +(P over P sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
2
An insect population starts at 500. Each subsequent yearly breeding season it grows by a certain percent. After 4 years it has increased to a population of 705.
Solve for the rate given this scenario?
a A LaTex expression showing 0 + r = +(P over P sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing 5 + r = +(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
d A LaTex expression showing 6 + r = +(P over P sub 0 ) to the power of 1 over t + 1
3
A rabbit population starts at 600. Each subsequent yearly breeding season it grows by a certain percent. After 2 years it has increased to a population of 648 rabbits.
Solve for the rate given this scenario?
a A LaTex expression showing 6 + r = +(P over P sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 8 + r = +(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 5 + r = +(P over P sub 0 ) to the power of t over 2 - 1
4
An insect population starts at 600. Each subsequent yearly breeding season it grows by a certain percent. After 2 years it has increased to a population of 661.
Solve for the rate given this scenario?
a A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 8 + r = +(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing 5 + r = +(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 0 + r = +(P over P sub 0 ) to the power of 1 over t + 1
5
An insect population starts at 200. Each subsequent yearly breeding season it grows by a certain percent. After 3 years it has increased to a population of 224.
Solve for the rate given this scenario?
a A LaTex expression showing 8 + r = +(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 6 + r = +(P over P sub 0 ) to the power of t over 2 - 1
6
A savings account starts with $500. Each subsequent year it earns a certain percent interest. After 2 years it has $594.
Solve for the rate given this scenario?
a A LaTex expression showing 4 + r = +(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 9 + r = +(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 3 + r = +(P over P sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
7
A rabbit population starts at 300. Each subsequent yearly breeding season it grows by a certain percent. After 7 years it has increased to a population of 344 rabbits.
Solve for the rate given this scenario?
a A LaTex expression showing 9 + r = +(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 5 + r = +(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing r = +(P over P sub 0 ) to the power of 1 over t - 1
d A LaTex expression showing 8 + r = +(P over P sub 0 ) to the power of 1 over t + 1
8
A credit card starts with $800 of debt. Each subsequent quarter it grows by a certain percent interest. After 2 quarters the debt has grown to $848.
Solve for the rate given this scenario?
a A LaTex expression showing r = +(D over D sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 8 + r = +(D over D sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 5 + r = +(D over D sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 8 + r = +(D over D sub 0 ) to the power of 1 over t + 1