Respuesta :
Using an exponential function, it is found that the projected growth rate is of 4.5%.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + k)^t[/tex]
In which:
- A(0) is the initial amount.
- k is the growth rate, as a decimal.
- t is the time, in years.
In this problem:
- Initially, the population, in millions, was of 23.9, hence [tex]A(0) = 23.9[/tex]
- After 10 years, it was of 37.1, hence [tex]t = 10, A(10) = 37.1[/tex]
We use the information given to solve for k.
[tex]A(t) = A(0)(1 + k)^t[/tex]
[tex]37.1 = 23.9(1 + k)^{10}[/tex]
[tex](1 + k)^{10} = \frac{37.1}{23.9}[/tex]
[tex]\sqrt[10]{(1 + k)^{10}} = \sqrt[10]{\frac{37.1}{23.9}}[/tex]
[tex]1 + k = \left(\frac{37.1}{23.9}\right)^{\frac{1}{10}}[/tex]
[tex]1 + k = 1.045[/tex]
[tex]k = 0.045[/tex]
The growth rate was of 4.5%.
A similar problem is given at https://brainly.com/question/25697660
