Solving for t

**jsu03** · February 1st 2010, 08:04 PM

Can someone help me solve for t. Thanks!

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

**Grandad** · February 2nd 2010, 10:37 AM

Hello jsu03

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:

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

$\Rightarrow 0.3010t = 9.5563$

$\Rightarrow t = 31.75$

Grandad

Thread: Solving for t