Question

a city has a population of 380,000 people. suppose that each year the population grows by 5.25%. 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 exponential growth

The formula for exponential growth is \( P(t) = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (as a decimal), and \( t \) is the time in years.
Here, \( P_0 = 380000 \), \( r = 0.0525 \) (since 5.25% = 0.0525), and \( t = 10 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 380000 \), \( r = 0.0525 \), and \( t = 10 \) into the formula:
\( P(10) = 380000(1 + 0.0525)^{10} \)
First, calculate \( 1 + 0.0525 = 1.0525 \).
Then, calculate \( 1.0525^{10} \). Using a calculator, \( 1.0525^{10} \approx 1.6681 \).

Step3: Multiply by the initial population

Multiply \( 380000 \) by \( 1.6681 \):
\( 380000 \times 1.6681 \approx 633878 \)

Answer:

633878