Question

The population of a county is growing at a rate of $9 %$ per year, compounded continuously. How many years will it take for the population to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.

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Answer

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Answer

Final Answer: $16$ years

Steps

Step 1 ：Translate the problem into the formula for continuous compounding: $P = P 0 * e^{r t}$

Step 2 ：Rearrange the formula to solve for t: $t = \frac{l n (P / P 0)}{r}$

Step 3 ：Substitute the given values into the formula: $t = \frac{l n (4)}{0.09}$

Step 4 ：Calculate the value of t: $t \approx 16$

Step 5 ：Round the answer up to the nearest whole number: $t = 16$

Step 6 ：Final Answer: $16$ years