Write an exponential function in the form y = ab that goes through points (0,18) and (2,288).

Question

Write an exponential function in the form y = ab that goes through points (0,18)

and (2,288).

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Aaliyah 3 hours 2021-10-13T03:51:14+00:00 1 Answer 0

Answers ( )

    0
    2021-10-13T03:52:55+00:00

    Answer:

     18 = ab^0 =a

    And using the second point we have this:

     288= 18 b^2

    If we divide both sides by 18 we got:

     16 = b^2

    And taking the square roof of 16 we got:

     b =\pm \sqrt{16} =\pm 4

    But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is:

     y = 18 (4)^x

    Step-by-step explanation:

    We want to construct an exponential function given by this general form:

     y = ab^x

    And we know that the function needs to pass for two points (0,18) and (2,288). Using the first point we have this:

     18 = ab^0 =a

    And using the second point we have this:

     288= 18 b^2

    If we divide both sides by 18 we got:

     16 = b^2

    And taking the square roof of 16 we got:

     b =\pm \sqrt{16} =\pm 4

    But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is:

     y = 18 (4)^x

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