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March 29, 2017

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if f is an exponential function, and f(5)=20 and f(9) = 14, use the add-multiply property to calculate f(13),f(17), and f(21). Show your method

  • Math - ,

    there is a difference of x=+4 between 5, 9
    There is a multiply difference of 14/20=.7 between the two.

    f(13)=14*.7
    f(17)=14*.7*.7
    f(21)=14(.7*.7*.7)

  • Math - ,

    let f(x) = a(b^x) or
    y = a(b^x)
    given: when x=5, y=20
    20 = a b^5
    given: when x=9, y=14
    14 = a b^9
    divide the 2nd by the first:
    b^4 = 14/20 = 0.7
    b = (0.7)^.25 = appr .91469
    sub into 20 = a b^5
    20 = a(.91469)^5
    a = 31.236
    f(x) = 31.236 (.91469)^x

    f(13) = 31.236(.91469)^13 = 9.8
    you do the button-pushing for the rest

    Note, I used the memory locations of my calculator to store all the supplied decimal values for both a and b

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