Question

a town has a population of 7000 and grows at 4% every year. what will be the population after 13 years, to the nearest whole number?

Explanation:

Step1: Identify growth formula

The compound growth formula is $P(t) = P_0(1 + r)^t$, where $P_0$ is initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Plug in given values

$P_0 = 7000$, $r = 0.04$, $t = 13$. Substitute into formula:
$P(13) = 7000(1 + 0.04)^{13}$

Step3: Calculate $(1.04)^{13}$

First compute $1.04^{13} \approx 1.66507$

Step4: Multiply by initial population

$7000 \times 1.66507 \approx 11655.49$

Step5: Round to nearest whole number

Round $11655.49$ to the nearest integer.

Answer:

11655