Question

a town has a population of 14000 and grows at 3.5% every year. what will be the population after 14 years, to the nearest whole number?

Explanation:

Step1: Identify the formula for compound growth

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

Step2: Convert the growth rate to decimal

The growth rate is 3.5%, so $r = \frac{3.5}{100} = 0.035$.

Step3: Substitute the values into the formula

Here, $P_0 = 14000$, $r = 0.035$, and $t = 14$. So we calculate $P(14) = 14000(1 + 0.035)^{14}$.

Step4: Calculate the exponent part

First, calculate $(1 + 0.035)^{14}$. Using a calculator, $(1.035)^{14}\approx1.618694$.

Step5: Multiply by the initial population

Now, multiply this by 14000: $14000\times1.618694\approx22661.716$.

Step6: Round to the nearest whole number

Rounding 22661.716 to the nearest whole number gives 22662.

Answer:

22662