Question

a town has a population of 12000 and grows at 5% every year. what will be the population after 12 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 \( r = 5\% = 0.05 \). The initial population \( P_0 = 12000 \), and time \( t = 12 \) years.

Step3: Substitute values into the formula

Substitute \( P_0 = 12000 \), \( r = 0.05 \), and \( t = 12 \) into the formula: \( P(12) = 12000(1 + 0.05)^{12} \).

Step4: Calculate the value

First, calculate \( (1.05)^{12} \approx 1.795856 \). Then, multiply by 12000: \( 12000 \times 1.795856 \approx 21550.27 \). Rounding to the nearest whole number gives 21550.

Answer:

21550