Question

Write the function for the graph.

(1,12)
(0,3)
O A. f(x) = 3•(12)^x
O B. f(x) = 4•(3)^x
O C. f(x) = 3•(4)^x
D. f(x) = 4•(12)^x

Answer 1

`f(x) =3 * (4)^x`

Explanation:

Given

`(x_1, y_1) = (1,12)`

`(x_2, y_2) = (0,3)`

Required

The function of the graph (exponential function)

An exponential function is represented as:

`f(x) = ab^x`

For
`(x_1, y_1) = (1,12)`, we have:

`12 = a * b^1`

`12 = a * b`

`12 = a b`

For
`(x_2, y_2) = (0,3)`

`3 = a * b^0`

`3 = a * 1`

`3 = a`

`a = 3`

Substitute:
`a = 3` in
`12 = a b`

`12 = 3 * b`

Divide both sides by 3

`4 = b`

`b =4`

So, we have:

`f(x) = ab^x`

`f(x) =3 * (4)^x`