Question

question
a town has a population of 20000 and grows at 4% every year. what will be the population after 6 years, to the nearest whole number?
answer

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, \( P_0 = 20000 \), \( r = 0.04 \) (since 4% = 0.04), and \( t = 6 \).

Step2: Substitute the values into the formula

Substitute \( P_0 = 20000 \), \( r = 0.04 \), and \( t = 6 \) into the formula:
\( P(6) = 20000(1 + 0.04)^6 \)

Step3: Calculate \( (1 + 0.04)^6 \)

First, calculate \( 1 + 0.04 = 1.04 \). Then, \( 1.04^6 \approx 1.265319018 \) (using a calculator or exponentiation rules).

Step4: Calculate the final population

Multiply the initial population by the growth factor:
\( P(6) = 20000 \times 1.265319018 \approx 25306.38 \)

Step5: Round to the nearest whole number

Rounding 25306.38 to the nearest whole number gives 25306.

Answer:

25306