The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

Question

3 years ago

13

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

rganism 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.

Mathematics

1 answer:

poizon [28] · Answer 1 · 2022-03-08T03:52:50+03:00

poizon [28]3 years ago

6 0

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