To model the scenario as an arithmetic sequence in explicit form, we can use the formula:
An = a1 + (n - 1) * d
where:
An represents the nth term of the sequence,
a1 is the first term of the sequence,
n is the number of terms in the sequence, and
d is the common difference between consecutive terms.
In this case, the first term (a1) is 8 feet, and the common difference (d) is 3 feet per year. Therefore, we have:
An = 8 + (n - 1) * 3
To rewrite the explicit form using function notation, we can replace An with f(n), and a1 with f(1). Our function would then be:
f(n) = f(1) + (n - 1) * d
Substituting the values, we have:
f(n) = 8 + (n - 1) * 3
Now, to find out how tall the tree will be in 12 years (f(12)), we plug in n = 12 into the function:
f(12) = 8 + (12 - 1) * 3
f(12) = 8 + 11 * 3
f(12) = 8 + 33
f(12) = 41 feet
The tree will be 41 feet tall after 12 years.