Exponential Function Solving - Growth (Continuous) Equation to Rate

Level 1

This math topic focuses on solving for the rate in exponential growth equations under continuous conditions. It involves using the natural exponential function \(e^x\) to model scenarios such as the growth of a rabbit population, the compounding growth of share prices, the increase in social media post views, and the proliferation of bacteria. Students are required to rearrange the exponential equation to isolate and solve for the rate \(r\), utilizing logarithmic transformations to linearize exponential growth data for easier computation. The problems are part of an introduction to exponential functions, and solutions are given in multiple-choice format.

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Exponential Function Solving - Growth (Continuous) Equation to Rate Worksheet

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Exponential Function Solving - Growth (Continuous) Equation to Rate
1
Solve for the rate given this model of a continuous growth of a rabbit population?
A LaTex expression showing 654 =500 times e to the power of (r times 9)
a A LaTex expression showing 3 + 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 3 + r = +\ln{\frac{P sub 0 over P }}{t}
2
Solve for the rate given this model of a continuously compounding growth of a share price?
A LaTex expression showing 866 =800 times e to the power of (r times 2)
a A LaTex expression showing 7 + r = +\ln{\frac{S sub 0 over S }}{t}
b A LaTex expression showing 1 + r = +e to the power of \frac{S over S sub 0 }{t}
c A LaTex expression showing 7 + r = +e to the power of \frac{S over S sub 0 }{t}
d A LaTex expression showing r = +\ln{\frac{S over S sub 0 }}{t}
3
Solve for the rate given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 254 =200 times e to the power of (r times 8)
a A LaTex expression showing 7 + r = +\ln{\frac{V sub 0 over V }}{t}
b A LaTex expression showing 4 + r = +\ln{\frac{V sub 0 over V }}{t}
c A LaTex expression showing 8 + r = +e to the power of \frac{V over V sub 0 }{t}
d A LaTex expression showing r = +\ln{\frac{V over V sub 0 }}{t}
4
Solve for the rate given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,144 =900 times e to the power of (r times 8)
a A LaTex expression showing 1 + r = +\ln{\frac{V sub 0 over V }}{t}
b A LaTex expression showing 1 + r = +e to the power of \frac{V over V sub 0 }{t}
c A LaTex expression showing 8 + r = +e to the power of \frac{V over V sub 0 }{t}
d A LaTex expression showing r = +\ln{\frac{V over V sub 0 }}{t}
5
Solve for the rate given this model of a continuous growth of a rabbit population?
A LaTex expression showing 1,014 =900 times e to the power of (r times 6)
a A LaTex expression showing 7 + r = +\ln{\frac{P sub 0 over P }}{t}
b A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}
c A LaTex expression showing 5 + r = +\ln{\frac{P sub 0 over P }}{t}
d A LaTex expression showing 1 + r = +e to the power of \frac{P over P sub 0 }{t}
6
Solve for the rate given this model of a continuous growth of a bacteria population?
A LaTex expression showing 1,044 =700 times e to the power of (r times 8)
a A LaTex expression showing 9 + r = +e to the power of \frac{P over P sub 0 }{t}
b A LaTex expression showing 1 + r = +\ln{\frac{P sub 0 over P }}{t}
c A LaTex expression showing 2 + r = +e to the power of \frac{P over P sub 0 }{t}
d A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}
7
Solve for the rate given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 858 =500 times e to the power of (r times 9)
a A LaTex expression showing 9 + r = +\ln{\frac{V sub 0 over V }}{t}
b A LaTex expression showing 7 + r = +e to the power of \frac{V over V sub 0 }{t}
c A LaTex expression showing 3 + r = +\ln{\frac{V sub 0 over V }}{t}
d A LaTex expression showing r = +\ln{\frac{V over V sub 0 }}{t}
8
Solve for the rate given this model of a continuous growth of a rabbit population?
A LaTex expression showing 1,254 =800 times e to the power of (r times 9)
a A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t}
b A LaTex expression showing 5 + r = +e to the power of \frac{P over P sub 0 }{t}
c A LaTex expression showing 6 + r = +e to the power of \frac{P over P sub 0 }{t}
d A LaTex expression showing 1 + r = +e to the power of \frac{P over P sub 0 }{t}