Question

Mateo is culturing bacteria that have a growth rate of 5.3% per hour. If the current population is 38,762 bacteria, how many bacteria will there be in 20 hours?If necessary, round your answer to the nearest whole number.

Answer 1

..Given:

$\begin{gathered} a=38762 \\ r=5.3\%=\frac{5.3}{100}=0.053 \\ t=20 \end{gathered}$

To Determine: The number of bacteria after 20 hours

Using the future value formula for growth rate

$\begin{gathered} P_a=P_c(1+r)^t \\ P_a=(Bacteria,final,population) \\ P_c(Bacteria,current,population)=38762 \\ r(rate)=0.053,t(time,in,hour)=20 \end{gathered}$

Therefore

$\begin{gathered} P_a=38762(1+0.053)^{20} \\ P_a=38762(1.053)^{20} \\ P_a=38762(2.809101) \\ P_a=108886.39 \\ P_a\approx108886 \end{gathered}$

Hence, population of bacteria in 20 hours is 108,886