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Exponential Function Growth (Continuous) - Equation to Scenario

Level 1

This math topic involves analyzing various real-world scenarios to match them with the appropriate exponential growth equations presented using continuous compounding. The problems include situations such as increasing downloads of an app, growth in a savings account balance, the expansion of a rabbit population, and the accumulation of credit card debt. Each problem presents an exponential growth equation and two possible scenarios, requiring the learner to select the scenario that fits the equation accurately. The focus is on understanding continuous growth rates (expressed as percentages) over specific periods.

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

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Exponential Function Growth (Continuous) - Equation to Scenario Worksheet

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Exponential Function Growth (Continuous) - Equation to Scenario
1
Which scenario describes this equation?
A LaTex expression showing 381 =300 times e to the power of (0.04 times 6)
a
An app starts with 300 downloads. Its download count grows continually by 4% each day.After 6 days it has 381 downloads.
b
An app starts with 400 downloads. Its download count grows continually by 3% each day.After 6 days it has 381 downloads.
2
Which scenario describes this equation?
A LaTex expression showing 514 =300 times e to the power of (0.06 times 9)
a
A savings account starts with $300. It grows continuously at 6% interest per month. After 9 months it has $514.
b
A savings account starts with $900. It grows continuously at 6% interest per month. After 3 months it has $514.
3
Which scenario describes this equation?
A LaTex expression showing 901 =800 times e to the power of (0.03 times 4)
a
A rabbit population starts at 800. It grows continuously at 3% growth per quarter. After 4 quarters it has increased to a population of 901 rabbits.
b
A rabbit population starts at 400. It grows continuously at 3% growth per quarter. After 8 quarters it has increased to a population of 901 rabbits.
4
Which scenario describes this equation?
A LaTex expression showing 429 =300 times e to the power of (0.09 times 4)
a
A credit card starts with $900 of debt. It grows continuously at 3% interest per month. After 4 months the debt has grown to $429.
b
A credit card starts with $300 of debt. It grows continuously at 9% interest per month. After 4 months the debt has grown to $429.
5
Which scenario describes this equation?
A LaTex expression showing 813 =700 times e to the power of (0.05 times 3)
a
A rabbit population starts at 300. It grows continuously at 5% growth per year. After 7 years it has increased to a population of 813 rabbits.
b
A rabbit population starts at 700. It grows continuously at 5% growth per year. After 3 years it has increased to a population of 813 rabbits.
6
Which scenario describes this equation?
A LaTex expression showing 381 =300 times e to the power of (0.06 times 4)
a
A savings account starts with $300. It grows continuously at 6% interest per month. After 4 months it has $381.
b
A savings account starts with $300. It grows continuously at 4% interest per month. After 6 months it has $381.
7
Which scenario describes this equation?
A LaTex expression showing 793 =600 times e to the power of (0.04 times 7)
a
A rabbit population starts at 600. It grows continuously at 4% growth per quarter. After 7 quarters it has increased to a population of 793 rabbits.
b
A rabbit population starts at 400. It grows continuously at 6% growth per quarter. After 7 quarters it has increased to a population of 793 rabbits.
8
Which scenario describes this equation?
A LaTex expression showing 442 =400 times e to the power of (0.05 times 2)
a
A company's share price starts at $200. It grows continuously at 5% growth per month. After 4 months it has a share price of $442.
b
A company's share price starts at $400. It grows continuously at 5% growth per month. After 2 months it has a share price of $442.