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Exponential Function Solving - Growth (Continuous) Scenario to Rate

Level 1

This math topic involves solving for continuous growth rates in various real-world scenarios. It focuses on exponential functions where students are required to calculate the rate of increase or interest based on the final and initial values over a given period of time. Problems include calculating the growth rates of insect populations, view counts on a social media post, company share prices, credit card debt, savings account balances, and app download counts. The mathematical operations primarily involve logarithmic calculations to determine the growth rate using the formula \( r = \ln\left(\frac{final value}{initial value}\right)/time \).

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 Rate Worksheet

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Exponential Function Solving - Growth (Continuous) Scenario to Rate
1
An insect population starts at 600. It grows continuously at a certain percent growth per day. After 7 days it has increased to a population of 793.
Solve for the rate given this scenario?
a A LaTex expression showing 0 + r = +e to the power of \frac{P over P sub 0 }{t}
b A LaTex expression showing 0 + r = +\ln{\frac{P sub 0 over P }}{t}
c A LaTex expression showing 6 + r = +\ln{\frac{P sub 0 over P }}{t}
d A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}
2
A social media post starts with 400 views. Its view count grows continually by a certain percent each year. After 7 years it has 751 views.
Solve for the rate given this scenario?
a A LaTex expression showing 7 + r = +\ln{\frac{V sub 0 over V }}{t}
b A LaTex expression showing r = +\ln{\frac{V over V sub 0 }}{t}
c A LaTex expression showing 2 + r = +\ln{\frac{V sub 0 over V }}{t}
d A LaTex expression showing 9 + r = +\ln{\frac{V sub 0 over V }}{t}
3
A company's share price starts at $900. It grows continuously at a certain percent growth per year. After 4 years it has a share price of $1,239.
Solve for the rate given this scenario?
a A LaTex expression showing 3 + r = +\ln{\frac{S sub 0 over S }}{t}
b A LaTex expression showing r = +\ln{\frac{S over S sub 0 }}{t}
c A LaTex expression showing 2 + r = +\ln{\frac{S sub 0 over S }}{t}
d A LaTex expression showing 4 + r = +\ln{\frac{S sub 0 over S }}{t}
4
A credit card starts with $400 of debt. It grows continuously at a certain percent interest per month. After 8 months the debt has grown to $469.
Solve for the rate given this scenario?
a A LaTex expression showing 7 + r = +\ln{\frac{D sub 0 over D }}{t}
b A LaTex expression showing 2 + r = +e to the power of \frac{D over D sub 0 }{t}
c A LaTex expression showing r = +\ln{\frac{D over D sub 0 }}{t}
d A LaTex expression showing 9 + r = +e to the power of \frac{D over D sub 0 }{t}
5
A savings account starts with $200. It grows continuously at a certain percent interest per year. After 3 years it has $261.
Solve for the rate given this scenario?
a A LaTex expression showing 0 + r = +e to the power of \frac{P over P sub 0 }{t}
b A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}
c A LaTex expression showing 9 + r = +\ln{\frac{P sub 0 over P }}{t}
d A LaTex expression showing 4 + r = +e to the power of \frac{P over P sub 0 }{t}
6
A social media post starts with 600 views. Its view count grows continually by a certain percent each week. After 3 weeks it has 785 views.
Solve for the rate given this scenario?
a A LaTex expression showing 9 + r = +\ln{\frac{V sub 0 over V }}{t}
b A LaTex expression showing 5 + r = +\ln{\frac{V sub 0 over V }}{t}
c A LaTex expression showing r = +\ln{\frac{V over V sub 0 }}{t}
d A LaTex expression showing 6 + r = +e to the power of \frac{V over V sub 0 }{t}
7
An app starts with 800 downloads. Its download count grows continually by a certain percent each week. After 6 weeks it has 1,217 downloads.
Solve for the rate given this scenario?
a A LaTex expression showing 4 + r = +e to the power of \frac{A over A sub 0 }{t}
b A LaTex expression showing r = +\ln{\frac{A over A sub 0 }}{t}
c A LaTex expression showing 0 + r = +e to the power of \frac{A over A sub 0 }{t}
d A LaTex expression showing 9 + r = +e to the power of \frac{A over A sub 0 }{t}
8
A rabbit population starts at 400. It grows continuously at a certain percent growth per year. After 8 years it has increased to a population of 646 rabbits.
Solve for the rate given this scenario?
a A LaTex expression showing 0 + r = +e to the power of \frac{P over P sub 0 }{t}
b A LaTex expression showing 7 + r = +\ln{\frac{P sub 0 over P }}{t}
c A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}