math - algebra

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f(t) is an exponential function with
f(0) = 200 and f(3) = 2000.

a) Use the form f(t) = Pe^rt to find the equation of this exponential function.

b) In the form f(x) = Pa^x, a is the growth factor. find the growth factor.

c)What input value gives an output value of 5,000?

  • math - algebra -

    mr.jagodnishvil

  • math - algebra -

    200 = Pe^0 = P
    2000 = Pe^rt = 200e^3r
    e^3r = 10
    3r = ln 10
    r = ln10/3 = 0.7675

    f(x) = 200a^x = 200e^.7675x
    a^x = e^.7675x
    a = e^.7675 = 2.154

    5000 = 2.154^x
    ln 5000 = x ln 2.154
    x = ln5000/ln2.154 = 11.1

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