Question 451664
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 80(0.613)^t]


We want A to be 40, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (0.613)^t\ =\ \frac{40}{80}\ =\ 0.5]


Take the log of both sides (I use ln, but base doesn't matter)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left((0.613)^t\right)\ =\ \ln(0.5)]


Use the properties of logarithms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ln(0.613)\ =\ \ln(0.5)]


And solve:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(0.5)}{\ln(0.613)}]


You can do your own arithmetic and rounding.


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