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: Recall the compound growth formula

The formula for compound growth is \( P = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (in decimal), \( t \) is the time in years, and \( P \) is the population after \( t \) years.

Step2: Identify the values

Here, \( P_0 = 10000 \), \( r = 5\% = 0.05 \), and \( t = 5 \).

Step3: Substitute the values into the formula

Substitute the values into the formula: \( P = 10000(1 + 0.05)^5 \).

Step4: Calculate \( (1 + 0.05)^5 \)

First, calculate \( 1 + 0.05 = 1.05 \). Then, \( 1.05^5 \approx 1.27628 \) (using a calculator).

Step5: Calculate the population \( P \)

Multiply by the initial population: \( P = 10000 \times 1.27628 = 12762.8 \).

Step6: Round to the nearest whole number

Rounding \( 12762.8 \) to the nearest whole number gives \( 12763 \).

Answer:

12763