Question

a town has a population of 16000 and grows at 4.5% every year. what will be the population after 8 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 (in decimal), \( t \) is the time in years, and \( P(t) \) is the population after \( t \) years.

Step2: Identify the values

Here, \( P_0 = 16000 \), \( r = 4.5\% = 0.045 \), and \( t = 8 \).

Step3: Substitute the values into the formula

Substitute the values into the formula: \( P(8) = 16000(1 + 0.045)^8 \).
First, calculate \( 1 + 0.045 = 1.045 \).
Then, calculate \( 1.045^8 \). Using a calculator, \( 1.045^8 \approx 1.42210061 \).

Step4: Calculate the final population

Multiply this by the initial population: \( P(8) = 16000 \times 1.42210061 \approx 22753.6098 \).
Rounding to the nearest whole number, we get \( 22754 \).

Answer:

The population after 8 years will be approximately \(\boxed{22754}\).