Question

The initial population of a town is 3000, and it grows with a doubling time of 10 years. What will the population be in 8 years?Please show step by step

Answer 1

Givens.

• The initial population is 3000. (P_0 = 3000)

,

• The ratio is 2 because it's doubling. (r = 2)

,

• The doubling time is 10 years. (u = 10)

,

• The total number of years is 8, t = 8.

Represent the problem with an exponential function because population growth has an exponential behavior.

$P(t)=P_0\cdot(r)^{\frac{t}{u}}$

Use the given values to find P(8).

$P(8)=3000\cdot(2)^{\frac{8}{10}}$

Then,

$\begin{gathered} P(8)=3000\cdot1.74110 \\ P(8)=5223.30 \end{gathered}$

Therefore, the population after 8 years is 5223.30.