# need help on solving exponential equations!

• Nov 12th 2007, 05:36 PM
zarlock99
need help on solving exponential equations!
heres the question, A mummified human body was recently found in a Scandinavian bog. Radioactive carbon was used to find the age of the mummy.
The amount of carbon-14 had decayed to 4^-1/3 of its original amount. The half life of carbon-14 is about 5370 years. For how long has the mummy been dead?
I know you use y=ab^x but i dont know how u use it for this question.
• Nov 12th 2007, 07:33 PM
TKHunny
Quote:

Originally Posted by zarlock99
heres the question, A mummified human body was recently found in a Scandinavian bog. Radioactive carbon was used to find the age of the mummy.
The amount of carbon-14 had decayed to 4^-1/3 of its original amount. The half life of carbon-14 is about 5370 years. For how long has the mummy been dead?
I know you use y=ab^x but i dont know how u use it for this question.

Plug it what is known.

$\frac{a}{2}\;=\;a*b^{4270}$

$\frac{1}{2}\;=\;b^{4270}$

$b\;=\;\left(\frac{1}{2}\right)^{-4270}$

Apply the mystery

$a*(4^{-1/3})\;=\;a*b^{x}$

Solve for x