SOLUTION: Suppose you invest $130 at 4% compounded continuously. a. Write an exponential function to model the amount in your investment account. b. Explain what each value in the function

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose you invest $130 at 4% compounded continuously. a. Write an exponential function to model the amount in your investment account. b. Explain what each value in the function      Log On


   

Question 468306: Suppose you invest $130 at 4% compounded continuously.
a. Write an exponential function to model the amount in your investment account.
b. Explain what each value in the function model represents.
c. In how many years will the total reach $600? Show your work.
Found 2 solutions by ewatrrr, Gogonati:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

invest $130 at 4% compounded continuously

 A = Pe^(rt) where P is the amount Invested, r the rate, t the number of years



$600 = $130 e^.04t

ln(600/130) = .04t

 1.5294/.04 = t

   38.2349yrs = t

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
The compounding continuously formula is: A%28t%29=P%2Ae%5E%28rt%29, where P is the
initial investment, r is the interest rate, and t the amount of time in years the
investment is held. To find in how many years the initial investment of $130 will
reach $600, we substitute in our formula A(t)=600, and get:
600=130%2Ae%5E%28.04t%29, solving this equation we get:60=13%2Ae%5E%28.04t%29<=>
60%2F13=e%5E%28.04t%29, taking the natural logarithms of both sides, we have
ln%2860%2F13%29=.04t, and final t=%28ln%2860%2F13%29%29%2F.04 or t=38 years.