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

Answer: D) $f(n)=8(1.5)^{n-1}$

Step-by-step 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

$f(2)=8(b)^{2-1}\\\Rightarrow12=8b\\\Rightarrow\ b=\frac{12}{8}\\\Rightarrow\ b=1.5$

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.

Answer 2

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.