Question

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5556 years. Suppose C(t) is the amount of carbon-14 present at time t. The exponential decay differential equation that models this scenario is C'=-kC . Solve the differential equation to answer the following questions.
(a) Find the value of the constant k in the differential equation.

Answer 1

As we know that the
 k = ln(2)/t½
so putting values
 = ln(2)/5556 years 
 =0.6931471/5556
 =0.0001247565yr⁻