math  algebra
posted by Alexis .
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?

(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