write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)

Question

write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)

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Kaylee 1 week 2021-11-26T05:10:03+00:00 1 Answer 0

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    2021-11-26T05:11:13+00:00

    Answer:

    see explanation

    Step-by-step explanation:

    The equation of the exponential function in the form

    y = ab^{x}

    Substitute the given points into the equation and solve for a and b

    Using (1, 7.5), then

    7.5 = ab → (1)

    Using (3, 16.875), then

    16.875 = ab³ → (2)

    Divide (2) by (1)

    \frac{ab^3}{ab} = \frac{16.875}{7.5}, hence

    b² = 2.25 ( take the square root of both sides )

    b = 1.5

    Substitute b = 1.5 into (1)

    1.5a = 7.5 ⇒ a = 5

    The exponential function is y = 5(1.5)^{x}

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