Calculus II: Exponential Change Problem?
Can you please help me with this problem:
The Charcoal From tree killed in the volcanic eruption that formed Crater Lake in Oregon contained 44.5% of the carbon-14 found in living matter. About how old in Crater Lake?

Question

bahrom7893 · Answer

The fraction of original amount present in a sample is
µ = y/y₀ 
= e^(- k·t )
<=>
t = - (1/k)·ln(µ)
= - 8266y · ln( 0.445 )
= 6693y

anonymous · Answer

where did that( - 8266y) come from :/

bahrom7893 · Answer

okay so:
t(1/2) = 5730 y <= half life of C14

bahrom7893 · Answer

1/k = t1/2 / ln(2) = 8266y

bahrom7893 · Answer

1/k = (t[1/2]) / ln(2) = 8266y

anonymous · Answer

oh ok i see...
but in the book..it says the answer is 6658 years..does it matter?

bahrom7893 · Answer

no, half life of C14 is not very precise... we'll always be off by several years, that's not really relevant

bahrom7893 · Answer

depends on how u round off, etc.. we are off by how many around 35 years. I know it seems a lot, but i think its fine. Fan me if I helped. Thanks

bahrom7893 · Answer

http://faculty.eicc.edu/bwood/ma155supplemental/supplemental5.htm btw just found ur exact problem there. they are getting ur book's answer, u might wanna take a look at example 4

anonymous · Answer

Thank you so much!
how do i fan you?

bahrom7893 · Answer

Click on Become a fan next to my name lol