Question

a town has a population of 2000 and grows at 4.5% every year. what will be the population after 13 years, to the nearest whole number?

Explanation:

Step1: Recall compound growth formula

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

Step2: Convert rate to decimal

$r = \frac{4.5}{100} = 0.045$

Step3: Plug values into formula

$P = 2000(1 + 0.045)^{13}$

Step4: Calculate the growth factor

First compute $1.045^{13} \approx 1.772196$

Step5: Compute final population

$P \approx 2000 \times 1.772196 = 3544.392$

Step6: Round to nearest whole number

Round 3544.392 to the nearest integer.

Answer:

3544