Question

a town has a population of 14000 and grows at 5% every year. what will be the population after 14 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 initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Identify given values

$P_0 = 14000$, $r = 0.05$, $t = 14$

Step3: Substitute values into formula

$P(14) = 14000(1 + 0.05)^{14}$

Step4: Calculate the growth factor

First compute $(1.05)^{14} \approx 1.979931599$

Step5: Compute final population

$P(14) = 14000 \times 1.979931599 \approx 27719.04239$

Step6: Round to nearest whole number

Round $27719.04239$ to the nearest integer.

Answer:

27719