Growth and Decay

Problem 209: Chris is a researcher at the Center for Disease Control and Prevention and he is trying to understand the behavior of a new and dangerous virus. He starts his experiment with 100 of the virus that grows at a rate of 25% per hour. He will check on the virus in 24 hours. How many viruses will he find?

Solution: One can find the amount of viruses can be found using the Growth and Decay formula

(1) $\begin{equation*} A_0 e^{rt}.\end{equation*}$

That is, $A_0 = 100$ , $r = 0.25$ , and $t = 24$ hours. Thus

(2) $\begin{align*} A_0 e^{rt} & = 100 e^{0.25 \cdot 24} \\ & = 100e^{6} \\ & = 40,343.\end{align*}$

This means that Chris will find 40,343 viruses when he check in 24 hours.

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