# math - algebra

posted by .

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

## Similar Questions

1. ### horizontal asymptote

Find the horizontal asymptotes of the function's graph y = 200 / (1+10e^(0.5x)) If you let x --> minus infinty the exponential tends to zero and the function approaches 200. If x --> infinity then the exponential becomes infinite …
2. ### Algebra

Describe how an exponential function changes as the base increases. What is an "exponential function" and how would I find the answer?
3. ### Algebra Help

Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x. Does this work?
4. ### MATH

State whether each equation in Exercises 25–30 represents a linear, quadratic, or exponential function. Tell how you decided. 3x^2=5 *I believe this equation is a exponential function but, I'm not sure how to explain it.*
5. ### math

find an exponential function of the form P(t)yoe^kt to model the given; In 1995, the number of female athletes participating in Summer Olympics-Type Games was 550. In 1996, about 3550 participated in the summer olympics in ATlanta. …
6. ### math - algebra

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 …
7. ### math - algebra

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 …
8. ### Math

Let f(t) be an exponential function with f(0) = 11 and f(4) = 59. Use the form f(t) = Pa^t to find an equation for this exponential function?
9. ### Exponential Growth and Decay

Can somebody please check my answers? 1. Identify the initial amount a and the growth factor b in the exponential function. g(x)=14*2^x a)a=14, b=x b)a=14, b=2 <<<< c)a=28, b=1 d)a=28, b=x 2. Identify the initial amount
10. ### Algebra

Construct exponential functiom of points (0,200) and (6,380). The exponential function is y(x)=____

More Similar Questions