Question

Jill has been watching the squirrels that live in her neighborhood. The number of squirrels changes each week.

n f(n)
1 8
2 12
3 18
4 27


Which function best shows the relationship between n and f(n)?
f(n) = 12(1.5)n
f(n) = 12(1.5)n−1
f(n) = 8(1.5)n
f(n) = 8(1.5)n−1

Answer 1

The answer is D

Step-by-step explanation:

Answer 2

Option D:
`f(n)=8(1.5)^(n-1)` is the function that represents the relationship between n and f(n)

Step-by-step 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.

`r=(12)/(8) =1.5`

`r=(18)/(12) =1.5`

`r=(27)/(18) =1.5`

Thus, the common difference are equal.

The equation of the function can be determined using the formula,

`a(n)=a(r)^(n-1)`

where a is the first term and r is the common difference.

Substituting the values, we have,

`a(n)=8(1.5)^(n-1)`

Hence, the function is given by

`f(n)=8(1.5)^(n-1)`

Thus, the function that represents the relationship between n and f(n) is
`f(n)=8(1.5)^(n-1)`

Therefore, Option D is the correct answer.