Question

a town has a population of 13000 and grows at 2.5% every year. what will be the population after 5 years, to the nearest whole number?

Explanation:

Step1: Recall the compound growth formula

The formula for compound growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate (as a decimal), $t$ is the time in years, and $P(t)$ is the population after $t$ years.

Step2: Identify the values

Here, $P_0 = 13000$, $r = 2.5\% = 0.025$, and $t = 5$.

Step3: Substitute the values into the formula

$P(5) = 13000(1 + 0.025)^5$

Step4: Calculate $(1 + 0.025)^5$

First, $1 + 0.025 = 1.025$. Then, $1.025^5 \approx 1.131408218$.

Step5: Calculate the population

$P(5) = 13000\times1.131408218 \approx 14708.30683$

Step6: Round to the nearest whole number

Rounding $14708.30683$ to the nearest whole number gives $14708$.

Answer:

14708