Question

What is the explicit function for the data in the table ?

Answer 1

Let's look at the info we have for each term:

term 1 = 4

term 2 = 12

term 3 = 36

term 4 = 108

term 5 = ?

Notice that term 2 (12) is obtained from the previous term 1 (4) by multiplying it by the number 3:

12 = 4 * 3

Now, term number 3 is obtained from term 2 (the previous) also by multiplying it by 3:

36 = 12 * 3

term number 4 is obtained from multiplying the previous term (term 3) by the number 3 again:

108 = 36 * 3

Now, we can conclude that if the strategy carries on, term number 5 will be the product of the pervious term (108) times 3. That is:

term 5 = 108 * 3 = 324

Now, we need to decide on which formula better describes our function:

We find that the function is better described by the formula:

`f(n)=(4)/(3)\cdot3^n`

since we can verify:

term 1 =

`(4)/(3)\cdot3^1=4`

term 2 =

`(4)/(3)\cdot3^2=12`

term 3 =

`(4)/(3)\cdot3^3=(4)/(3)\cdot27=36`

term 4 =

`(4)/(3)\cdot3^4=(4)/(3)\cdot81=108`

So the correct answer is the second option they give you in the list.