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.

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 (as a decimal), and \( t \) is the time in years.
Here, \( P_0 = 240000 \), \( r = 0.0675 \) (since \( 6.75\% = \frac{6.75}{100}=0.0675 \)), and \( t = 10 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 240000 \), \( r = 0.0675 \), and \( t = 10 \) into the formula:
\( P=240000\times(1 + 0.0675)^{10} \)
First, calculate \( 1+ 0.0675=1.0675 \)
Then, calculate \( 1.0675^{10} \). Using a calculator, \( 1.0675^{10}\approx1.92147 \)

Step3: Calculate the final population

Multiply \( 240000 \) by \( 1.92147 \):
\( P = 240000\times1.92147 = 461152.8 \)

Step4: Round to the nearest whole number

Rounding \( 461152.8 \) to the nearest whole number gives \( 461153 \)

Answer:

\( 461153 \)