Question

*Help* Whats The Answer To This Graph?

Answer 1

C

Explanation:

Answer 2

C. The growth factor of g is twice the growth factor of f.

Explanation:

Let's find the growth factor of g(x) by getting its equation. To do it, we are using the standard exponential equation:

`y=a(b+1)^x`

where

`a` is the initial value

`b` is the growth factor

We know form our graph that g(x) passes throughout (0, 3), so
`x=0` and
`y=3`.

Replacing values

`3=a(b+1)^0`

`3=a(1)`

`a=3`

We also know from our graph the g(x) passes throughout (1, 12), so
`x=1` and
`y=12`.

Replacing values

`y=a(b+1)^x`

`12=3(b+1)^1`

`12=3(b+1)`

`b+1=(12)/(3)`

`b+1=4`

`b=4-1`

`b=3`

The growth factor of g(x) is 4.

Now, to find the growth factor of f(x), we just need to equate 1+b with
`(5)/(2)` and solve for b:

`1+b=(5)/(2)`

`b=(5)/(2) -1`

`b=(3)/(2)`

`b=1.5`

Finally, we can divide the growth factor of g(x) by the growth factor of f(x) to find how many times bigger is the growth factor of g(x):

`(3)/(1.5) =2`

We can conclude that the growth factor of g is twice the growth factor of f.