Algebra Story Problem - may use expotential logrithms?
Assume that the amount of Carbon 14 absorbed in a tree several centuries ago is the same as the amount absorbed in a tree growing today. Suppose a piece of ancient charcoal which contains only 20% as much of the radioactive carbon as a piece of modern charcoal is found. How long ago did the tree burn to make this ancient charcoal? Assume the half-life of Carbon 14 is 5730 years.
I know... seriously?? Right?
Update:Can you show me how to work through it.... I know pullling that stuff back into your brain will hurt but, it would mean a lot to me :)
Answers & Comments
Verified answer
20% = 0.20
Find n such that (½)ⁿ = 0.20. n is the number of half-lives since the tree was burned.
(½)ⁿ = 0.20
2⁻ⁿ = 0.20
log₂(2⁻ⁿ) = log₂(0.20)
(−n)log₂(2) = log₂(0.20)
−n = -2.322
n = 2.322
2.322 half-lives × 5730 years per half-life = 13305 years
Lol, there is an equation for this... it's a logarithm. Nice that I'm in calc and don't have to do this crap anymore :). But, um, to an estimation, the tree burned a little over 22920 years ago (that'd be if it had 25% as much radioactive carbon). i'd guess about 25,000 years.
There is a log equation for this, you can just plug crap in.