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Math Help - Solving for t

  1. #1
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    Solving for t

    Can someone help me solve for t. Thanks!

    (.5)^-(t)/(4.5*10^9) * 100 = 80
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello jsu03
    Quote Originally Posted by jsu03 View Post
    Can someone help me solve for t. Thanks!

    (.5)^-(t)/(4.5*10^9) * 100 = 80
    I take it that the equation is:
    \frac{(0.5)^{-t}}{4.5\times10^9}\times100=80
    So divide both sides by 100:
    \frac{(0.5)^{-t}}{4.5\times10^9}=0.8
    \Rightarrow (0.5)^{-t}=0.8\times4.5\times10^9
    =3.6\times10^9
    Take logs (to base 10) of both sides:
    -t\log(0.5) =\log(3.6)+9

    \Rightarrow 0.3010t = 9.5563

    \Rightarrow t = 31.75
    Grandad
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