Question

a town has a population of 12000 and grows at 5% every year. what will be the population after 12 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 initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Identify given values

$P_0 = 12000$, $r = 0.05$, $t = 12$

Step3: Substitute values into formula

$P = 12000(1 + 0.05)^{12}$

Step4: Calculate the growth factor

First compute $(1.05)^{12} \approx 1.795856$

Step5: Compute final population

$P = 12000 \times 1.795856 \approx 21550.27$

Step6: Round to nearest whole number

Round 21550.27 to 21550

Answer:

21550