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Maria, a biologist is observing the growth pattern of a virus. She starts with $100$ of the virus that grows at a rate of $10\%$ per hour. She will check on the virus in $24$ hours. How many viruses will she find?

She will find

viruses.

Solution

First, we identify the values of each variable: $A_{0}=100\text{,}$ $r=0.10\text{/hour}\text{,}$ and $t=24\text{ hours}\text{.}$

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

$\begin{aligned} A\amp=A_{0}e^{rt}\\ \amp=\substitute{100}e^{\substitute{0.10}\cdot \substitute{24}}\\ \amp\approx 1102\text{ viruses} \end{aligned}$