Answer:
[tex]y = 13(5)^x[/tex]
Step-by-step explanation:
We are given the following exponential function:
[tex]y = ab^x[/tex]
(0,13)
This means that when [tex]x = 0, y = 13[/tex]. So
[tex]y = ab^x[/tex]
[tex]13 = ab^0[/tex]
[tex]a = 13[/tex]
Then
[tex]y = 13b^x[/tex]
(2,325)
This means that when [tex]x = 2, y = 325[/tex] We use this to find b. So
[tex]y = 13b^x[/tex]
[tex]13b^2 = 325[/tex]
[tex]b^2 = \frac{325}{13}[/tex]
[tex]b^2 = 25[/tex]
[tex]b = 5[/tex]
Thus
[tex]y = 13(5)^x[/tex]
