Question

a town has a population of 5000 and grows at 3.5% every year. what will be the population after 15 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), and \( t \) is the number of years.
Here, \( P_0 = 5000 \), \( r = 0.035 \) (since \( 3.5\% = \frac{3.5}{100}=0.035 \)), and \( t = 15 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 5000 \), \( r = 0.035 \), and \( t = 15 \) into \( P(t)=P_0(1 + r)^t \):
\( P(15)=5000\times(1 + 0.035)^{15} \)

Step3: Calculate \( (1 + 0.035)^{15} \)

First, calculate \( 1+0.035 = 1.035 \). Then, find \( 1.035^{15} \). Using a calculator, \( 1.035^{15}\approx1.675348 \)

Step4: Calculate the final population

Multiply \( 5000 \) by \( 1.675348 \):
\( P(15)=5000\times1.675348 = 8376.74 \)

Step5: Round to the nearest whole number

Rounding \( 8376.74 \) to the nearest whole number gives \( 8377 \).

Answer:

\( 8377 \)