# Solving for t

• February 1st 2010, 08:04 PM
jsu03
Solving for t
Can someone help me solve for t. Thanks!

(.5)^-(t)/(4.5*10^9) * 100 = 80
• February 2nd 2010, 10:37 AM
Hello jsu03
Quote:

Originally Posted by jsu03
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:
$-t\log(0.5) =\log(3.6)+9$

$\Rightarrow 0.3010t = 9.5563$

$\Rightarrow t = 31.75$