Question

A researcher at the Center for Disease Control and Prevention is studying the growth of a bacteria. He starts his experiment with $100$of the bacteria that grows at a rate of $6\%$per hour. He will check on the bacteria every $8$hours. How many bacteria will he find in $8$hours?

Short answer

The researcher will find$162$bacteria in$8$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.

Substitute P=1000,r=0.06,t=8 in the formula.

$$\begin{gathered} A=1000{\left(e\right)}^{0.06.8} \\ =1000{\left(e\right)}^{0.48} \\ \approx 162 \end{gathered}$$

Therefore, the researcher will find$162$bacteria in$8$hours.