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

Step2: Identify given values

$P_0 = 2000$, $r = 0.045$, $t = 13$

Step3: Substitute values into formula

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

Step4: Calculate growth factor first

$(1.045)^{13} \approx 1.772196$

Step5: Compute final population

$2000 \times 1.772196 \approx 3544.39$

Step6: Round to nearest whole number

Round $3544.39$ to the nearest integer.

Answer:

3544