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alexandr402 [8]
2 years ago
6

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

Mathematics
1 answer:
sineoko [7]2 years ago
6 0

Answer:

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

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that exponential function

                  y = a bˣ ...(i)

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

               9 = a (b )⁰ = a

             a =9

<u><em>Step(ii):-</em></u>

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

<u><em>Final answer:-</em></u>

An exponential function in the form y=abˣ

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

<u><em></em></u>

<u><em>   </em></u>

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