Question

a town has a population of 14000 and grows at 3% every year. what will be the population after 6 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, \( P_0 = 14000 \), \( r = 0.03 \) (since 3% = 0.03), and \( t = 6 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 14000 \), \( r = 0.03 \), and \( t = 6 \) into \( P(t) = P_0(1 + r)^t \):
\( P(6) = 14000(1 + 0.03)^6 \)

Step3: Calculate \( (1 + 0.03)^6 \)

First, calculate \( 1.03^6 \). Using a calculator, \( 1.03^6 \approx 1.1940522965 \)

Step4: Multiply by the initial population

Multiply 14000 by 1.1940522965:
\( P(6) = 14000 \times 1.1940522965 \approx 16716.732151 \)

Step5: Round to the nearest whole number

Rounding 16716.732151 to the nearest whole number gives 16717.

Answer:

16717