Question

a city has a population of 240,000 people. suppose that each year the population grows by 6.75%. what will the population be after 10 years? use the calculator provided and round your answer to the nearest whole number. people

Explanation:

Step1: Identify the formula for population growth

The formula for compound population growth is \( P = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the annual growth rate (in decimal), and \( t \) is the time in years.
Here, \( P_0 = 240000 \), \( r = 6.75\% = 0.0675 \), and \( t = 10 \).

Step2: Substitute the values into the formula

Substitute the values into the formula: \( P = 240000(1 + 0.0675)^{10} \).
First, calculate \( 1 + 0.0675 = 1.0675 \).
Then, calculate \( 1.0675^{10} \). Using a calculator, \( 1.0675^{10} \approx 1.9216 \).

Step3: Calculate the final population

Multiply the initial population by the growth factor: \( P = 240000 \times 1.9216 \approx 461184 \).

Answer:

461184