Question

a town has a population of 14000 and grows at 2.5% every year. what will be the population after 5 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, $t$ is time in years.

Step2: Identify given values

$P_0 = 14000$, $r = 0.025$, $t = 5$

Step3: Substitute values into formula

$P = 14000(1 + 0.025)^5 = 14000(1.025)^5$

Step4: Calculate $(1.025)^5$

$(1.025)^5 \approx 1.13140821$

Step5: Compute final population

$P \approx 14000 \times 1.13140821 = 15839.71494$

Step6: Round to nearest whole number

Round $15839.71494$ to the nearest integer.

Answer:

15840