Question 356135
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Good start.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10,000\ =\ 5000\left(1\ +\ \frac{0.05}{4}\right)^{4t}]


Divide both sides by 5000 and do the arithmetic inside of the parentheses:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(1.0125\right)^{4t}\ =\ 2]


Now take the log of both sides.  You can use *[tex \Large \log_{10}] or *[tex \Large \ln] -- Doesn't matter, you get the same answer either way.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(1.0125\right)^{4t}\ =\ \ln(2)]


Now use:  


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4t\ln\left(1.0125\right)\ =\ \ln(2)]


Then divide both sides by *[tex \Large 4\ln\left(1.0125\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(2)}{4\ln\left(1.0125\right)}]


Now all you have left is a little calculator work.  Let me know what you got.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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