Question

a city has a population of 320,000 people. suppose that each year the population grows by 4.25%. what will the population be after 5 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 (in decimal), and \( t \) is the time in years.

Step2: Convert the growth rate to decimal

The growth rate \( r = 4.25\% = 0.0425 \). The initial population \( P_0 = 320000 \), and \( t = 5 \) years.

Step3: Substitute the values into the formula

Substitute \( P_0 = 320000 \), \( r = 0.0425 \), and \( t = 5 \) into the formula: \( P(5) = 320000(1 + 0.0425)^5 \).
First, calculate \( 1 + 0.0425 = 1.0425 \). Then, calculate \( 1.0425^5 \). Using a calculator, \( 1.0425^5 \approx 1.2312 \) (more precise calculation: \( 1.0425^5 = 1.0425\times1.0425\times1.0425\times1.0425\times1.0425 \approx 1.23116 \)).
Then, multiply by the initial population: \( 320000\times1.23116 \approx 393971.2 \).

Step4: Round to the nearest whole number

Rounding \( 393971.2 \) to the nearest whole number gives \( 393971 \).

Answer:

393971