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

Level 1

This math topic revolves around solving exponential growth scenarios using continuous growth models. It includes calculations of final values for scenarios such as app downloads growing annually, credit card debt accumulating interest each quarter, and bacteria populations increasing daily or annually. The problems require applying the exponential growth formula \( A = A_0 \times e^{(rt)} \), where \( A_0 \) is the initial amount, \( r \) is the rate of growth, and \( t \) is the time elapsed. These practices are fundamental in understanding how quantities evolve over time in continuously compounding situations, emphasizing exponential functions' practical applications in finance, population studies, and other growth phenomena.

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

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

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Exponential Function Solving - Growth (Continuous) Scenario to Value ...
1
An app starts with 700 downloads. Its download count grows continually by 9% each year.After 2 years it has a larger number of downloads.
Solve for the final downloads given this scenario?
a A LaTex expression showing 5 + A = A sub 0 - e to the power of (r times t)
b A LaTex expression showing 1 + A = A sub 0 - e to the power of (r times t)
c A LaTex expression showing A = A sub 0 times e to the power of (r times t)
2
A credit card starts with $300 of debt. It grows continuously at 4% interest per quarter. After 2 quarters the debt has grown to a certain amount.
Solve for the final debt given this scenario?
a A LaTex expression showing 2 + D = D sub 0 - e to the power of (r times t)
b A LaTex expression showing 0 + D = D sub 0 times e to the power of (r over t )
c A LaTex expression showing D = D sub 0 times e to the power of (r times t)
d A LaTex expression showing 4 + D = D sub 0 - e to the power of (r times t)
3
A credit card starts with $900 of debt. It grows continuously at 2% interest per quarter. After 4 quarters the debt has grown to a certain amount.
Solve for the final debt given this scenario?
a A LaTex expression showing 9 + D = D sub 0 times e to the power of (r over t )
b A LaTex expression showing 5 + D = D sub 0 - e to the power of (r times t)
c A LaTex expression showing 3 + D = D sub 0 - e to the power of (r times t)
d A LaTex expression showing D = D sub 0 times e to the power of (r times t)
4
A bacteria population starts at 700. It grows continuously at 6% growth per year. After 4 years it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 9 + P = P sub 0 - 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 P = P sub 0 times e to the power of (r times t)
5
A bacteria population starts at 200. It grows continuously at 8% growth per day. After 7 days it has increased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 8 + P = P sub 0 - e to the power of (r times t)
b A LaTex expression showing 4 + P = P sub 0 times e to the power of (r over t )
c A LaTex expression showing 6 + P = P sub 0 times e to the power of (r over t )
d A LaTex expression showing P = P sub 0 times e to the power of (r times t)
6
An app starts with 600 downloads. Its download count grows continually by 7% each month.After 3 months it has a larger number of downloads.
Solve for the final downloads given this scenario?
a A LaTex expression showing 7 + A = A sub 0 times e to the power of (r over t )
b A LaTex expression showing 8 + A = A sub 0 - e to the power of (r times t)
c A LaTex expression showing A = A sub 0 times e to the power of (r times t)
7
A savings account starts with $700. It grows continuously at 5% interest per month. After 8 months it has a certain amount of cash.
Solve for the final cash given this scenario?
a A LaTex expression showing 0 + 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 5 + P = P sub 0 times e to the power of (r over t )
8
A credit card starts with $200 of debt. It grows continuously at 8% interest per month. After 5 months the debt has grown to a certain amount.
Solve for the final debt given this scenario?
a A LaTex expression showing 6 + D = D sub 0 - e to the power of (r times t)
b A LaTex expression showing D = D sub 0 times e to the power of (r times t)
c A LaTex expression showing 7 + D = D sub 0 times e to the power of (r over t )
d A LaTex expression showing 5 + D = D sub 0 times e to the power of (r over t )