Question 236622
A woman deposits 50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled.
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A(t) = Pe^(rt)
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Explanation of the variables.
A(t) is the value of the account after t years.
P is the amount initially deposited in the account
e = 2.1718281828... is an irrational number that comes up in
the math modeling of growing or decaying things like money accounts.
r is the yearly interest rate 
t is the number of years the account is compounded.
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100,000 = 50,000*e^(0.04t)
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e^(0.04t) = 2
Note: The natural log of e^x is x because "ln(e^x)" means
tell me the exponent of e that gives you e^x.  The answer is "x".
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Take the natural log of both sides to get:
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ln(e^0.04t) = ln(2)
0.04t = ln2
t = [ln(2)/0.04]
t = 17.33 years
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Cheers,
stan H.