Name: Catherine Sullivan Question: Please help me with the following: The radioactive isotope carbon14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon12 at a rate proportional to the amount of C14 present, with a half life of 5730 years. Suppose C(t) is the amount of C14 at time t.
Note: for part 1, I know how to solve for k using the equation C=C*e^{kt}, but I need to do it from the differential equation. I took the integral of both sides but was left with a first derivative and too many unknowns. Please help!! Thanks Hi Catherine,C is the amount of carbon14 that is present at time t. (Sometimes it helps to write C(t) to emphasize that it is a function of t.) Start with the differential equation C' = k C and divide both sides by C to get Integrate both sides with respect to t and the equation becomes Integration produces where H is a constant. Now solve for C by taking the expontanial of each side and you get where A is the constant e^{H}. Thus you have the equation C = A e^{k t} which you can solve for k. Cheers,Harley
