Question 302801
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It doesn't matter how much you deposit, the time to double your investment is the same whether you deposit 10 cents or 10 million dollars.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ Pe^{rt}]


And we want


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 2P]


Therefore we need to find the value of *[tex \LARGE t] that makes *[tex \LARGE e^{rt}\ =\ 2] when *[tex \LARGE r\ =\ 0.04], so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ e^{0.04t}\ =\ 2]


Take the natural log of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(e^{0.04t}\right)\ =\ \ln(2)]


Log of an argument raised to a power is the power times the log of the argument.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ {0.04t}\ln\left(e^\right)\ =\ \ln(2)]


But *[tex \LARGE ln(e)\ =\ 1], so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(2)}{0.04}]


Just use your calculator



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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