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)?.A) f(n) = 12(1.5)n. B) f(n) = 12(1.5)n-1. C) f(n) = 8(1.5)n. D) f(n) = 8(1.5)n-1

Answer 1

We are given with the data on teh number of squirrels seen in each week. In this case, the number of squirrels seen increases as week goes. This is a geometric series with a ratio of 1.5 and a1 equal to 8. The equation should be 8 (1.5)^(n-1) where n is the number of weeks. The answer is option D. 

Answer 2

Answer: D)
`f(n)=8(1.5)^(n-1)`

Explanation:

From the given table we can see that this is not representing a linear function as the rate of change is not constant.

So it can be exponential growth function
`A(b)^(n-1)`, where A is the initial amount , b is the multiplicative rate of growth and n is the time period in weeks.

Now here at n=1 , f(n)=8

Therefore, A=8

Now, for n=2

`f(2)=8(b)^(2-1)\\\Rightarrow12=8b\\\Rightarrow\ b=(12)/(8)\\\Rightarrow\ b=1.5`

By substitute the values of A and b in the above equation, we get the equation
`f(n)=8(1.5)^(n-1)`

Therefore, the function best shows the relationship between n and f(n) is

`f(n)=8(1.5)^(n-1)`, where n is the number of weeks.