SOLUTION: The level of thorium in a sample decrases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The level of thorium in a sample decrases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is      Log On


   

Question 165540: The level of thorium in a sample decrases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is the meteorite?
I am totally lost on this one. Can you help me?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you start with 100% (1.00)

after 4.2 million years, you have 50% (.50) or 1 * .5 or (.5)^1

after another 4.2 million years, you have 25% (.25) or 1 * .5 * .5 or (.5)^2

after N cycles (they're called half-lives) you have (.5)^N remaining

(.5)^N=.076 __ taking log __ N(log(.5))=log(.076) __ dividing by log(.5) __ N=(log(.076))/(log(.5))

using a calculator __ N=3.7 (approx)

so the age of the meteorite is N times 4.2 million or 15.5 million (approx)