Question

question 5 - 1 point
in 2011, the population of a district was 31,600. with a continuous annual growth rate of approximately 2%, what will the population be in 2021 according to the exponential growth function?
round the answer to the nearest whole number.
provide your answer below:
people

Explanation:

Step1: Identify the formula

The formula for continuous growth is \( P(t)=P_0e^{rt} \), where \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is the time.

Step2: Determine the values

\( P_0 = 31600 \), \( r=0.02 \), \( t = 2021 - 2011=10 \)

Step3: Substitute into the formula

\( P(10)=31600\times e^{0.02\times10}=31600\times e^{0.2} \)

Step4: Calculate \( e^{0.2} \)

Using a calculator, \( e^{0.2}\approx1.221402758 \)

Step5: Find \( P(10) \)

\( P(10)=31600\times1.221402758\approx38606.33725 \)

Answer:

\( 38606 \)