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A park started with 12 oak trees, and the number of oak trees increased at a rate of [tex]$25\%$[/tex] each year. Write the function that models the situation, substituting numerical values for [tex]$A$[/tex] and [tex][tex]$r$[/tex][/tex] into the expression.

[tex]
f(x) = A(1 + r)^x
[/tex]

[tex]
f(x) = 12(1 + 0.25)^x
[/tex]



Answer :

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]