SOLUTION: I am having issues with word problems, just not sure how to set them up and then complete. Radioactive carbon-14 decays according to the function Q(t)=Q0e^-0.000121t where t is

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am having issues with word problems, just not sure how to set them up and then complete. Radioactive carbon-14 decays according to the function Q(t)=Q0e^-0.000121t where t is      Log On


   

Question 1027427: I am having issues with word problems, just not sure how to set them up and then complete.
Radioactive carbon-14 decays according to the function Q(t)=Q0e^-0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Q0 is the amount present at t=0. Estimate the age of bone fragment if 17% of the original quantity of carbon-14 remains.
Thank you for all your help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
They are saying that +Q%28t%29+=+.17Q%280%29+. This means,
at present, you have 17% of the amount you started with
which was +Q%280%29+
----------------------
Now I can rewrite the formula:
+Q%28t%29+=+Q%280%29%2Ae%5E%28-.000121t+%29+
+.17Q%280%29+=+Q%280%29%2Ae%5E%28-.000121t+%29+
Now divide both sides by +Q%280%29+
+.17+=+e%5E%28-.000121t+%29+
Take the natural log of both sides
+ln%28+.17+%29+=+-.000121t+
+-1.772+=+-.000121t+
+t+=+1.772+%2F+.000121+
+t+=+14644.628+
The age is 14,645 years
Check my math & maybe get another opinion