Question

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

Answer 1

Answer:

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

         ⇒    $\frac{576}{9} = b^{3}$

      ⇒     64 = b³

     ⇒     4³ = b³

             $(4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }$

             b = 4

Final answer:-

An exponential function in the form y=abˣ

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