Growth and Decays II

Problem 210: A research at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with 50 of the bacteria that grows at a rate of 15% per hour. She will check on the bacteria every 8 hours. How many bacteria will he find 8 in 8 hours?

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, $A_0 = 50$ , $r = 0.15$ , and $t = 8$ hours. Thus

(2) $\begin{align*} A_0 e^{rt} & = 50 e^{0.15 \cdot 8} \\ & = 50e^{1.2} \\ & = 166.\end{align*}$

This means that Lisa will find 166 viruses when he check in 8 hours.

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