Question

a town has a population of 16000 and grows at 4.5% every year. what will be the population after 8 years, to the nearest whole number?

Explanation:

Step1: Define growth formula

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

Step2: Identify given values

$P_0 = 16000$, $r = 0.045$, $t = 8$

Step3: Substitute values into formula

$P(8) = 16000(1 + 0.045)^8$

Step4: Calculate the growth factor

First compute $(1.045)^8 \approx 1.422100613$

Step5: Compute final population

$P(8) = 16000 \times 1.422100613 \approx 22753.61$

Step6: Round to nearest whole number

Round $22753.61$ to the nearest integer.

Answer:

22754