Question

a town has a population of 11000 and grows at 4% every year. what will be the population after 15 years, to the nearest whole number?

Explanation:

Step1: Identify 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: Plug in given values

$P_0 = 11000$, $r = 0.04$, $t = 15$. Substitute:
$P(15) = 11000(1 + 0.04)^{15}$

Step3: Calculate $(1.04)^{15}$

First compute $1.04^{15} \approx 1.8009435$

Step4: Multiply by initial population

$11000 \times 1.8009435 \approx 19810.38$

Step5: Round to nearest whole number

Round $19810.38$ to the nearest integer.

Answer:

19810