To model the situation where the number of oak trees in a park increases by 25% each year from an initial number of 12 trees, we can write the function using the general exponential growth formula [tex]\( f(x) = A(1 + r)^x \)[/tex]. Here, [tex]\( A \)[/tex] represents the initial number of oak trees, and [tex]\( r \)[/tex] is the annual growth rate.
Given:
- [tex]\( A = 12 \)[/tex] (initial number of oak trees)
- [tex]\( r = 0.25 \)[/tex] (growth rate per year as a decimal)
Substitute these values into the formula:
[tex]\[
f(x) = 12(1 + 0.25)^x
\][/tex]
This simplifies to:
[tex]\[
f(x) = 12(1.25)^x
\][/tex]
Therefore, the function that models the number of oak trees in the park after [tex]\( x \)[/tex] years is:
[tex]\[
f(x) = 12(1.25)^x
\][/tex]
