Question

complete the table shown to the right for the population growth model for a certain country. the projected 2039 population is (square) million. (round to one decimal place as needed.)

Explanation:

Step1: Find the number of years

The number of years from 2005 to 2039 is \(t = 2039 - 2005=34\) years.

Step2: Use the population growth formula

The population growth formula is \(P = P_0e^{kt}\), where \(P_0 = 84.1\) (initial population in 2005), \(k = 0.0065\) (growth rate), and \(t = 34\).
Substitute the values into the formula: \(P=84.1e^{0.0065\times34}\).
First, calculate \(0.0065\times34 = 0.221\).
Then, \(e^{0.221}\approx1.247\) (using a calculator for the exponential function).
Now, \(P = 84.1\times1.247\).
\(84.1\times1.247=(80 + 4.1)\times1.247=80\times1.247+4.1\times1.247=99.76+5.1127 = 104.8727\).

Answer:

\(104.9\)