Question

a town has a population of 5000 and grows at 2% 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 \( P = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (in decimal), and \( t \) is the time in years.
Here, \( P_0 = 5000 \), \( r = 0.02 \) (since 2% = 0.02), and \( t = 5 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 5000 \), \( r = 0.02 \), and \( t = 5 \) into the formula:
\( P = 5000(1 + 0.02)^5 \)

Step3: Calculate \( (1 + 0.02)^5 \)

First, calculate \( 1 + 0.02 = 1.02 \). Then, \( 1.02^5 \approx 1.1040808032 \)

Step4: Calculate the final population

Multiply the initial population by the growth factor:
\( P = 5000 \times 1.1040808032 \approx 5520.404016 \)

Step5: Round to the nearest whole number

Rounding \( 5520.404016 \) to the nearest whole number gives 5520.

Answer:

5520