Question

question
a town has a population of 5000 and grows at 2% 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 \( P(t)=P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (in decimal), and \( t \) is the time in years.
Here, \( P_0 = 5000 \), \( r=\frac{2}{100}=0.02 \), and \( t = 5 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 5000 \), \( r = 0.02 \), and \( t = 5 \) into \( P(t)=P_0(1 + r)^t \).
We get \( P(5)=5000\times(1 + 0.02)^5 \).

Step3: Calculate \( (1 + 0.02)^5 \)

First, calculate \( 1+0.02 = 1.02 \). Then, \( 1.02^5\approx1.1040808032 \) (using a calculator to find the fifth power of 1.02).

Step4: Calculate the population after 5 years

Multiply \( 5000 \) by \( 1.1040808032 \): \( 5000\times1.1040808032 = 5520.404016 \).

Step5: Round to the nearest whole number

Rounding \( 5520.404016 \) to the nearest whole number gives \( 5520 \).

Answer:

5520