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

Level 1

This math topic focuses on solving exponential growth equations to find the starting value in various contexts, such as population growth, credit card debt, and compound interest. Problems involve deciphering a given exponential model and selecting the correct formula for recalculating the initial quantity. Each question is presented with multiple choice answers where students must manipulate exponential expressions to isolate the initial value. The variety of scenarios highlights practical applications of exponential growth, reinforcing theoretical understanding through real-world examples.

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

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Exponential Function Solving - Growth (Discrete) Equation to Starting Value Worksheet

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Exponential Function Solving - Growth (Discrete) Equation to Starting...
1
Solve for the starting population given this model of a growth of a rabbit population (yearly breeding cycle)?
A LaTex expression showing 993 =P sub 0 times (1+0.02) to the power of (5)
a A LaTex expression showing 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 7 + P sub 0 = P times (1+r) to the power of t
d A LaTex expression showing 9 + P sub 0 = P over (1-r) to the power of t
2
Solve for the starting debt given this model of a growth in credit card debt with quarterly interest?
A LaTex expression showing 684 =D sub 0 times (1+0.04) to the power of (8)
a A LaTex expression showing 8 + D sub 0 = D over (1-r) to the power of t
b A LaTex expression showing 1 + D sub 0 = D over (1-r) to the power of t
c A LaTex expression showing 4 + D sub 0 = D over (1-r) to the power of t
d A LaTex expression showing D sub 0 = D over (1+r) to the power of t
3
Solve for the starting population given this model of a growth of a rabbit population (yearly breeding cycle)?
A LaTex expression showing 684 =P sub 0 times (1+0.04) to the power of (8)
a A LaTex expression showing 7 + P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing P sub 0 = P over (1+r) to the power of t
c A LaTex expression showing 6 + P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing 9 + P sub 0 = P over (1-r) to the power of t
4
Solve for the starting population given this model of a growth of an insect population that breeds once per year?
A LaTex expression showing 1,122 =P sub 0 times (1+0.07) to the power of (5)
a A LaTex expression showing 6 + P sub 0 = P times (1+r) to the power of t
b A LaTex expression showing 5 + 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
5
Solve for the starting cash given this model of a monthly compounding growth of money in a savings account?
A LaTex expression showing 1,033 =P sub 0 times (1+0.02) to the power of (7)
a A LaTex expression showing 7 + P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 5 + 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
d A LaTex expression showing P sub 0 = P over (1+r) to the power of t
6
Solve for the starting population given this model of a growth of a rabbit population (yearly breeding cycle)?
A LaTex expression showing 562 =P sub 0 times (1+0.04) to the power of (3)
a A LaTex expression showing 1 + P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing P sub 0 = P over (1+r) to the power of t
c A LaTex expression showing 2 + 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
7
Solve for the starting population given this model of a growth of a rabbit population (yearly breeding cycle)?
A LaTex expression showing 1,204 =P sub 0 times (1+0.06) to the power of (5)
a A LaTex expression showing 0 + P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 1 + 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
8
Solve for the starting population given this model of a growth of an insect population that breeds once per year?
A LaTex expression showing 936 =P sub 0 times (1+0.06) to the power of (5)
a A LaTex expression showing 2 + P sub 0 = P times (1+r) to the power of t
b A LaTex expression showing 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 8 + P sub 0 = P times (1+r) to the power of t