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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 - ,

    (a) If f(t) = Pe^(rt)
    200 = P^0 = P (Therefore P = 200)
    2000 = 200 e^(3r)
    e^3r = 10
    3r = ln10 = 2.303
    r = 0.76753

    The equation is
    f(t) = 200*e^(0.76753 t)

    (b) 2000 = 200*a^3
    a^3 = 10
    a = 2.15443
    y = 200*(2.15443)^x

    (c) Solve 5000 = 200*2.15443^x
    25 = 2.15443^x
    x = ln25/ln2.15443 = 4.1938

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