Question

the population of a country was 288 million in 1991 and the continuous exponential growth rate was estimated at 2.2% per year. assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1998. round your answer to 1 decimal place. the approximate population in 1998 is million people question help: video

Explanation:

Step1: Identify the formula for exponential growth

The formula for continuous exponential 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 of \( P_0 \), \( r \), and \( t \)

Given \( P_0 = 288\) million, \( r=0.022\) (since \( 2.2\%=0.022 \)), and \( t = 1998 - 1991=7\) years.

Step3: Substitute the values into the formula

\( P(7)=288e^{0.022\times7}\)
First, calculate \( 0.022\times7 = 0.154\)
Then, \( e^{0.154}\approx1.166\) (using a calculator for \( e^x \))
\( P(7)=288\times1.166 = 335.808\)

Answer:

\( 335.8\)