Answer:
[tex]y=9 ( {2}^{x} )[/tex]
Step-by-step explanation:
Let the exponential function be
[tex]y = a {b}^{x} [/tex]
We substitute (0,9) to get:
[tex]9 = a {b}^{0} [/tex]
[tex]9 = a(1)[/tex]
[tex]a = 9[/tex]
The equation now becomes:
[tex]y = 9 {b}^{x} [/tex]
We substitute (3,72) to get:
[tex]72 =9 {b}^{3} [/tex]
[tex]8={b}^{3} \\ {2}^{3} = {b}^{3} [/tex]
[tex]b = 2[/tex]
The equation is therefore
[tex]y=9 ( {2}^{x} )[/tex]
