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Exponential Function Solving - Growth (Discrete) Scenario to Starting Value

Level 1

This math topic focuses on solving exponential growth scenarios to determine the initial value of a quantity. The problems involve calculating the starting populations of rabbits and insects, the initial amount of debt on credit cards, and the starting cash in a savings account based on their growth over time at specified rates. The exercises require an understanding of exponential functions and involve reversing the exponential growth formula to find the original value before growth occurred. Each question is presented with multiple-choice solutions involving mathematical expressions for students to select the correct formula and solution.

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 Starting Value Worksheet

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Exponential Function Solving - Growth (Discrete) Scenario to Starting...
1
A rabbit population starts at a certain size. Each subsequent yearly breeding season it grows by 9%. After 8 years it has increased to a population of 1,195 rabbits.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing 4 + P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 6 + P sub 0 = P times (1+r) to the power of t
d A LaTex expression showing 8 + P sub 0 = P times (1+r) to the power of t
2
An insect population starts at a certain size. Each subsequent yearly breeding season it grows by 9%. After 4 years it has increased to a population of 988.
Solve for the starting population given this scenario?
a A LaTex expression showing 5 + P sub 0 = P times (1+r) to the power of t
b A LaTex expression showing 5 + P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 7 + P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing P sub 0 = P over (1+r) to the power of t
3
A credit card starts with a certain amount of debt. Each subsequent month it grows by 6% in interest. After 3 months the debt has grown to $952.
Solve for the starting debt given this scenario?
a A LaTex expression showing 1 + D sub 0 = D over (1-r) to the power of t
b A LaTex expression showing 5 + D sub 0 = D over (1-r) to the power of t
c A LaTex expression showing 2 + D sub 0 = D times (1+r) to the power of t
d A LaTex expression showing D sub 0 = D over (1+r) to the power of t
4
A credit card starts with a certain amount of debt. Each subsequent quarter it grows by 6% in interest. After 9 quarters the debt has grown to $1,182.
Solve for the starting debt given this scenario?
a A LaTex expression showing D sub 0 = D over (1+r) to the power of t
b A LaTex expression showing 9 + D sub 0 = D times (1+r) to the power of t
c A LaTex expression showing 3 + D sub 0 = D times (1+r) to the power of t
d A LaTex expression showing 7 + D sub 0 = D over (1-r) to the power of t
5
An insect population starts at a certain size. Each subsequent yearly breeding season it grows by 4%. After 2 years it has increased to a population of 540.
Solve for the starting population given this scenario?
a A LaTex expression showing 1 + P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 0 + P sub 0 = P times (1+r) to the power of t
c A LaTex expression showing P sub 0 = P over (1+r) to the power of t
6
A credit card starts with a certain amount of debt. Each subsequent year it grows by 3% in interest. After 7 years the debt has grown to $491.
Solve for the starting debt given this scenario?
a A LaTex expression showing 4 + D sub 0 = D times (1+r) to the power of t
b A LaTex expression showing 9 + D sub 0 = D over (1-r) to the power of t
c A LaTex expression showing D sub 0 = D over (1+r) to the power of t
d A LaTex expression showing 7 + D sub 0 = D over (1-r) to the power of t
7
A savings account starts with a certain amount of cash. Each subsequent month it earns 5% in interest. After 4 months it has $243.
Solve for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing 5 + P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 2 + P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing 3 + P sub 0 = P times (1+r) to the power of t
8
An insect population starts at a certain size. Each subsequent yearly breeding season it grows by 8%. After 7 years it has increased to a population of 514.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing 8 + P sub 0 = P times (1+r) to the power of t
c A LaTex expression showing 3 + P sub 0 = P times (1+r) to the power of t