Question

A biologist is observing the growth pattern of a virus. She starts with $50$of the virus that grows at a rate of $20\%$per hour. She will check on the virus in $24$hours. How many viruses will she find?

Short answer

She will find$6076$virus in$24$hours.

Step-by-step solution

Step 1 The formula for the compounded continuously is,

$A=P{\left(e\right)}^{rt}$

where $A$is the new balance.

$P$is the principal.

$r$is the interest rate.

$t$is the number of years.

Step 2 Substitute P=50,r=0.2,t=24 in the formula.

$$\begin{gathered} A=50{\left(e\right)}^{0.2\left(24\right)} \\ =50{\left(e\right)}^{4.8} \\ \approx 6076 \end{gathered}$$

Therefore, she will find $6076$virus in $24$hours.