Question

Write an exponential function in the form y

and (3,72).
ab" that goes through points (0,9)

Answer 1

`y=9 ( {2}^(x) )`

Explanation:

Let the exponential function be

`y = a {b}^(x)`

We substitute (0,9) to get:

`9 = a {b}^(0)`

`9 = a(1)`

`a = 9`

The equation now becomes:

`y = 9 {b}^(x)`

We substitute (3,72) to get:

`72 =9 {b}^(3)`

`8={b}^(3) \\ {2}^(3) = {b}^(3)`

`b = 2`

The equation is therefore

`y=9 ( {2}^(x) )`