Question

a town has a population of 18000 and grows at 2% every year. what will be the population after 11 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 initial population, $r$ is annual growth rate, and $t$ is time in years.

Step2: Identify given values

$P_0 = 18000$, $r = 0.02$, $t = 11$

Step3: Substitute values into formula

$P = 18000(1 + 0.02)^{11}$

Step4: Calculate the growth factor

First compute $(1.02)^{11} \approx 1.24337414$

Step5: Compute final population

$P = 18000 \times 1.24337414 \approx 22380.7345$

Step6: Round to nearest whole number

Round $22380.7345$ to the nearest integer.

Answer:

22381