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Exponential Function Solving - Growth (Continuous) Equation to Value at Time

Level 1

This math topic covers solving exponential growth problems using the continuous growth model. Specifically, it involves calculating the future value of different populations (such as bacteria, rabbits, and insects) and other quantities like social media post views and credit card debt. Each question provides an initial value and a growth rate, applying the formula \( P = P_0 e^{rt} \) to solve for the final amount after a certain period of time. The questions are arranged to enhance understanding of continuous exponential growth equations and their practical applications in various real-world scenarios.

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

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Exponential Function Solving - Growth (Continuous) Equation to Value at Time Worksheet

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Exponential Function Solving - Growth (Continuous) Equation to Value ...
1
Solve for the final population given this model of a continuous growth of a bacteria population?
A LaTex expression showing P =700 times e to the power of (0.06 times 3)
a A LaTex expression showing P = P sub 0 times e to the power of (r times t)
b A LaTex expression showing 7 + P = P sub 0 - e to the power of (r times t)
c A LaTex expression showing 5 + P = P sub 0 times e to the power of (r over t )
2
Solve for the final population given this model of a continuous growth of a rabbit population?
A LaTex expression showing P =200 times e to the power of (0.05 times 8)
a A LaTex expression showing 7 + P = P sub 0 - e to the power of (r times t)
b A LaTex expression showing P = P sub 0 times e to the power of (r times t)
c A LaTex expression showing 3 + P = P sub 0 times e to the power of (r over t )
d A LaTex expression showing 4 + P = P sub 0 - e to the power of (r times t)
3
Solve for the final population given this model of a continuous growth of an insect population?
A LaTex expression showing P =900 times e to the power of (0.06 times 2)
a A LaTex expression showing 6 + P = P sub 0 - e to the power of (r times t)
b A LaTex expression showing P = P sub 0 times e to the power of (r times t)
c A LaTex expression showing 5 + P = P sub 0 - e to the power of (r times t)
d A LaTex expression showing 4 + P = P sub 0 times e to the power of (r over t )
4
Solve for the final views given this model of a continuous exponential growth of social media post views?
A LaTex expression showing V =200 times e to the power of (0.08 times 6)
a A LaTex expression showing 6 + V = V sub 0 times e to the power of (r over t )
b A LaTex expression showing 4 + V = V sub 0 times e to the power of (r over t )
c A LaTex expression showing 0 + V = V sub 0 - e to the power of (r times t)
d A LaTex expression showing V = V sub 0 times e to the power of (r times t)
5
Solve for the final population given this model of a continuous growth of an insect population?
A LaTex expression showing P =900 times e to the power of (0.05 times 3)
a A LaTex expression showing P = P sub 0 times e to the power of (r times t)
b A LaTex expression showing 6 + P = P sub 0 - e to the power of (r times t)
c A LaTex expression showing 0 + P = P sub 0 times e to the power of (r over t )
d A LaTex expression showing 7 + P = P sub 0 times e to the power of (r over t )
6
Solve for the final population given this model of a continuous growth of a bacteria population?
A LaTex expression showing P =700 times e to the power of (0.06 times 5)
a A LaTex expression showing 7 + P = P sub 0 times e to the power of (r over t )
b A LaTex expression showing P = P sub 0 times e to the power of (r times t)
c A LaTex expression showing 0 + P = P sub 0 times e to the power of (r over t )
d A LaTex expression showing 8 + P = P sub 0 - e to the power of (r times t)
7
Solve for the final debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing D =300 times e to the power of (0.04 times 9)
a A LaTex expression showing 8 + D = D sub 0 times e to the power of (r over t )
b A LaTex expression showing 3 + D = D sub 0 - e to the power of (r times t)
c A LaTex expression showing D = D sub 0 times e to the power of (r times t)
8
Solve for the final debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing D =900 times e to the power of (0.08 times 2)
a A LaTex expression showing D = D sub 0 times e to the power of (r times t)
b A LaTex expression showing 3 + D = D sub 0 - e to the power of (r times t)
c A LaTex expression showing 9 + D = D sub 0 times e to the power of (r over t )
d A LaTex expression showing 7 + D = D sub 0 - e to the power of (r times t)