Respuesta :
Using an exponential function, it is found that the population of the town in 2020 will be of 495.
What is an exponential function?
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem:
- The population of a small town is 567 in 2011, hence [tex]A(0) = 567[/tex].
- The population decreases at a rate of 1.5% every year, hence [tex]r = 0.015[/tex].
Then:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 567(1 - 0.015)^t[/tex]
[tex]A(t) = 567(0.985)^t[/tex]
2020 is 9 years after 2011, hence:
[tex]A(9) = 567(0.985)^9 = 495[/tex]
The population of the town in 2020 will be of 495.
You can learn more about exponential functions at https://brainly.com/question/25537936
