Question

a town has a population of 2000 and grows at 4% every year. what will be the populat 15 years, to the nearest whole number?

Explanation:

Step1: Recall compound growth formula

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

Step2: Identify given values

$P_0 = 2000$, $r = 0.04$, $t = 15$

Step3: Substitute values into formula

$P = 2000(1 + 0.04)^{15}$

Step4: Calculate the growth factor

First compute $(1.04)^{15} \approx 1.8009435$

Step5: Compute final population

$P = 2000 \times 1.8009435 = 3601.887$

Step6: Round to nearest whole number

Round $3601.887$ to the nearest integer.

Answer:

3602