Posted by **Alexis** on Tuesday, November 1, 2011 at 7:11am.

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 -
**Henry**, Wednesday, November 2, 2011 at 9:30pm
F(t) = Pe^rt

a. F(0) = P*e^0 = 200,

P*e^0 = 200,

P*1 = 200,

P = 200.

F(3) = 200*e^3r = 2000,

200e^3r = 2000,

Divide both sides by 200:

e^3r = 10,

Take Ln of both sides:

3r*Lne = Ln10,

3r = Ln10 / Lne = 2.30259 / 1 = 2.3026,

r = 0.7675.

Eq: F(t) = 200e^(0.7675t).

b. F(x) = 200a^x.

F(3) = 200a^3 = 2000,

200a^3 = 2000,

a^3 = 10,

a = 2.15443.

Eq: F(x) = 200(2.15443)^x

c. F(x) = 200a^x = 5000,

200a^x = 5000,

a^x = 25,

Take Log of botn sides:

x*Loga = Log25,

X = Log25 / Loga=Log25 / Log(2.15443),

X = 4.194.

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