The correct function to model the population t years after 2015 is: f(t) = 53,792 * (1.025)^t
Here's the breakdown:
53,792: This represents the initial population in 2015.
(1.025)^t: This represents the population growth factor.
^t: This represents the number of years that have passed since 2015.
The population increases by 2.5% annually, which means it is multiplied by 1.025 every year.
Therefore, after t years, the population will be the initial population multiplied by the growth factor raised to the power of t.
This is why the correct function is f(t) = 53,792 * (1.025)^t.
Incorrect options:
Of(t) = 53, 792(1.25) t: This incorrectly uses 1.25 as the growth factor instead of 1.025.
Of(t) = 1.02t+ 53,792: This incorrectly includes an additional term of 1.02t, which is not part of the exponential growth model.
Therefore, the function f(t) = 53,792 * (1.025)^t accurately models the population of Macon County t years after 2015