Answer :
We have a population of 200,000 people that increase by 6%. We have to calculate the population after 11 years.
We can model the population at year t as:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]where P0 is the population of 200,000 and r is the growth rate r = 0.06.
Wecan calculate the population after 11 years as:
[tex]\begin{gathered} P(11)=P_0\cdot(1+r)^{11} \\ P(11)=200000\cdot(1+0.06)^{11} \\ P(11)=200000\cdot1.06^{11} \\ P(11)\approx200000\cdot1.8983 \\ P(11)\approx379660 \end{gathered}[/tex]Answer: the population after 11 years will be 379660.