Assume that the half life of C-14 is 5730 years using standard C-14 techniques , a certain animal bone contian

20% of the C-14 it originally is expected to have had when the animal was alive.rounded to the nearest hundred years,how many years ago did the animal live????

Assume that the half life of C-14 is 5730 years using standard C-14 techniques , a certain animal bone contian
Hello,





Lets use a = p(1 -r)(^n) where a is the amount remaining p is the original amount r is the rate of decay and n is the number of years.





So when it is half gone we have:





.5 = 1(1-r)^5730 then taking the 5730 root of both sides gives us (.5)^(1/5730) = 1 -r





then 0.9999 = 1 - r so r = 0.0001 then putting it back in gives us.


.20 = 1 (1 - 0.0001)^x now





.20 = 1 (0.9999)^x take the log of both sides





log.20 = log(0.9999)^x but the log of a power is the power times the log so





log .20 = x log(0.9999) then x = log.20/log(0.9999)





x = 16093.57 rounded to the nearest 100 yeras would be





16100 years ago.





Hope This Helps!!