Question

a town has a population of 2000 and grows at 4% 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 growth rate (in decimal), and \( t \) is the time in years.
Here, \( P_0 = 2000 \), \( r = 0.04 \) (since 4% = 0.04), and \( t = 15 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 2000 \), \( r = 0.04 \), and \( t = 15 \) into the formula:
\( P(15) = 2000(1 + 0.04)^{15} \)

Step3: Calculate \( (1 + 0.04)^{15} \)

First, calculate \( 1.04^{15} \). Using a calculator, \( 1.04^{15} \approx 1.800943 \)

Step4: Calculate the final population

Multiply this by 2000: \( 2000 \times 1.800943 \approx 3601.886 \)

Step5: Round to the nearest whole number

Rounding 3601.886 to the nearest whole number gives 3602.

Answer:

3602