..Given:
[tex]\begin{gathered} a=38762 \\ r=5.3\%=\frac{5.3}{100}=0.053 \\ t=20 \end{gathered}[/tex]To Determine: The number of bacteria after 20 hours
Using the future value formula for growth rate
[tex]\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}[/tex]Therefore
[tex]\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}[/tex]Hence, population of bacteria in 20 hours is 108,886
