SOLUTION: Suppose $4000.00 is invested at interest rate K, compounded continuously, and grows to $4943.71 in 6 years: Find the interest rate. Find the exponential growth function. Find th

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Question 531391: Suppose $4000.00 is invested at interest rate K, compounded continuously, and grows to $4943.71 in 6 years:
Find the interest rate.
Find the exponential growth function.
Find the balance after 10 years.
Find the doubling time.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose $4000.00 is invested at interest rate K, compounded continuously, and grows to $4943.71 in 6 years:
---
A(t) = Ao*e^(rt)
4943.71 = 4000*e^(6K)
e^(6K) = 1.2359
6K = ln(1.2359)
K = 0.0353
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Find the interest rate:::3.53%
Find the exponential growth function.A(t) = 4000*e^(0.0353t)
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Find the balance after 10 years.A(10) =4000*e^(0.353) = $5693.32
----------------------------
Find the doubling time.
e^(0.0353t) = 2
0.0353t = ln2
t = 19.64 years
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Cheers,
Stan H.