Can someone help me solve for t. Thanks!

(.5)^-(t)/(4.5*10^9) * 100 = 80

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- Feb 1st 2010, 08:04 PMjsu03Solving for t
Can someone help me solve for t. Thanks!

(.5)^-(t)/(4.5*10^9) * 100 = 80 - Feb 2nd 2010, 10:37 AMGrandad
Hello jsu03I take it that the equation is:

$\displaystyle \frac{(0.5)^{-t}}{4.5\times10^9}\times100=80$So divide both sides by $\displaystyle 100$:

$\displaystyle \frac{(0.5)^{-t}}{4.5\times10^9}=0.8$

$\displaystyle \Rightarrow (0.5)^{-t}=0.8\times4.5\times10^9$Take logs (to base $\displaystyle 10$) of both sides:$\displaystyle =3.6\times10^9$

$\displaystyle -t\log(0.5) =\log(3.6)+9$Grandad

$\displaystyle \Rightarrow 0.3010t = 9.5563$

$\displaystyle \Rightarrow t = 31.75$