Question

a town has a population of 10000 and grows at 5% every year. what will be the population after 5 years, to the nearest whole number?

Explanation:

Step1: Identify compound growth formula

Population after \( n \) years: \( P = P_0(1 + r)^n \)

Step2: Plug in values

\( P_0 = 10000 \), \( r = 0.05 \), \( n = 5 \) → \( P = 10000(1 + 0.05)^5 \)

Step3: Calculate \( (1.05)^5 \)

\( 1.05^5 ≈ 1.27628 \)

Step4: Compute final population

\( 10000 × 1.27628 ≈ 12763 \) (rounded)

Answer:

12763