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Mathematics 50 Online
OpenStudy (anonymous):

After t years, the annual sales in hundreds of thousands of units of product q is given by q=(1/2)^(.8)^t 2) After how many years will the annual sales be about 95,350 units? Show your work. (Hint: You will have to take the log of both sides twice.)

OpenStudy (unklerhaukus):

\[q=\left(\frac12\right)^{.8^t}\] \[\log_{1/2}q=.8^t\] \[\log_{0.8}\left(\log_{1/2}\left(q\right)\right)=t\] \[t=\log_{0.8}\left(\log_{1/2}\left(95350\right)\right)\]

OpenStudy (anonymous):

2,781 years?

OpenStudy (unklerhaukus):

\[t=\frac{\log_{10}\left(\frac{\log_{10}\left(95350\right)}{\log_{10}(1/2) }\right)}{\log_{10}(0.8)}\]

OpenStudy (anonymous):

how sure are you?

OpenStudy (anonymous):

how did you get to there?

OpenStudy (unklerhaukus):

which step didn't you follow/?

OpenStudy (anonymous):

how you got to the new formula

OpenStudy (unklerhaukus):

take the log of both sides to base 1/2 take the log of both sides to base 0.8

OpenStudy (unklerhaukus):

i used the change of base formula in the last step so a calculator that only has base 10 could be used

OpenStudy (anonymous):

hmm i keep getting error

OpenStudy (unklerhaukus):

for some reason im not getting a real answer either

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