Question

a town has a population of 17000 and grows at 4% 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 (as a decimal), \( t \) is the time in years, and \( P(t) \) is the population after \( t \) years.

Step2: Identify the values

Here, \( P_0 = 17000 \), \( r = 0.04 \) (since 4% = 0.04), and \( t = 5 \).

Step3: Substitute the values into the formula

\( P(5)=17000\times(1 + 0.04)^5 \)
First, calculate \( (1 + 0.04)^5=(1.04)^5 \approx 1.2166529024 \)
Then, \( P(5)=17000\times1.2166529024 \approx 20683.0993408 \)

Step4: Round to the nearest whole number

Rounding \( 20683.0993408 \) to the nearest whole number gives 20683.

Answer:

20683