Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

Step(i):-

Given that exponential function

                  y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

               9 = a (b )⁰ = a

             a =9

Step(ii):-

The equation (i) passes through the point (3,576)

            576 = 9(b)³

         ⇒    

      ⇒     64 = b³

     ⇒     4³ = b³

             b = 4

Final -

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)