Question

The initial population of a town is 3100 , and it grows with a doubling time of 10 years. What will the population be in 12 years?Question content area bottomPart 1What will the population be in 12 years?  enter your response here(Round to the nearest whole number as needed.)

Answer 1

Explanation

An exponential model for population growth has the following model:

$P=P_0(1+r)^t$

Therefore; since the town has a population growth that doubles in 10 years

$\begin{gathered} 2P_0=P_0(1+r)^{10} \\ 2=(1+r)^{10} \\ \sqrt[10]{2}=\sqrt[10]{(1+r)^{10}} \\ 1.07177=1+r \end{gathered}$

In 12 years, we will have

$\begin{gathered} P=3100\left(1.07177\right)^{\left\{12\right\}} \\ P=7121.65370 \\ P=7122 \end{gathered}$

Answer: 7122