Option D: [tex]f(n)=8(1.5)^{n-1}[/tex] is the function that represents the relationship between n and f(n)
Explanation:
Let n represents the weeks
Let f(n) represents the number of squirrels.
We need to determine the function that represents the relationship between n and f(n)
The given sequence is a geometric sequence.
First, we shall determine the common difference.
[tex]r=\frac{12}{8} =1.5[/tex]
[tex]r=\frac{18}{12} =1.5[/tex]
[tex]r=\frac{27}{18} =1.5[/tex]
Thus, the common difference are equal.
The equation of the function can be determined using the formula,
[tex]a(n)=a(r)^{n-1}[/tex]
where a is the first term and r is the common difference.
Substituting the values, we have,
[tex]a(n)=8(1.5)^{n-1}[/tex]
Hence, the function is given by
[tex]f(n)=8(1.5)^{n-1}[/tex]
Thus, the function that represents the relationship between n and f(n) is [tex]f(n)=8(1.5)^{n-1}[/tex]
Therefore, Option D is the correct answer.
