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Another researcher 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 she find in $8$ hours?

She will find

bacteria.

Solution

First, we identify the values of each variable: $A_{0}=50\text{,}$ $r=0.15\text{/hour}\text{,}$ and $t=8\text{ hours}\text{.}$

Next, we substitute these values into the formula and simplify, $A=A_{0}e^{rt}\text{:}$

$\begin{aligned} A\amp=A_{0}e^{rt}\\ \amp=\substitute{50}e^{\substitute{0.15}\cdot \substitute{8}}\\ \amp\approx 166\text{ bacteria} \end{aligned}$