SOLUTION: Suppose that ​$10,095 is invested at an interest rate of 6.2​% per​ year, compounded continuously. ​a) Find the exponential function that describes the amo

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Question 1120705: Suppose that ​$10,095 is invested at an interest rate of 6.2​% per​ year, compounded continuously.
​a) Find the exponential function that describes the amount in the account after time​ t, in years.
​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years?
​c) What is the doubling​ time?
I don't know how to set up the formula. Once the formula is set up I know that I substitute the number into t.
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Suppose that ​$10,095 is invested at an interest rate of 6.2​% per​ year, compounded continuously.
​a) Find the exponential function that describes the amount in the account after time​ t, in years.
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V(t) = P*e^t
P = 10,095, e = 2.718281828459045....
​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years?
---------------------
​c) What is the doubling​ time?
Solve e^t = 2
t = ln(2)/ln(e) = ln(2) = 0.693 yrs
--------------------------------
I don't know how to set up the formula. Once the formula is set up I know that I substitute the number into t.
-----------
Cheers,
Stan H.
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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Suppose that ​$10,095 is invested at an interest rate of 6.2​% per​ year, compounded continuously.
​a) Find the exponential function that describes the amount in the account after time​ t, in years.
​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years?
​c) What is the doubling​ time?
I don't know how to set up the formula. Once the formula is set up I know that I substitute the number into t.
Correct formula: , where:

P = $10,095

e = 2.7182818.......

r = Annual interest rate (6.2%, or .062, in this case)

t = time



What is wrong with these people on here? How can an amount take less than 1 YEAR to double? RIDICULOUS!!

At a rate of 6.2%, and with CONTINUOUS compounding, ANY investment/deposit will take  to DOUBLE! 

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