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.
There is also Part B, if anybody can get (a) 1

Answer 1

decay y=e^(-kt)
growth y=e^(+kt)

you have decay so

C=e^(-kt) fits.

C'=-k*e^(-kt)=-k*C also fits.

now to find k:
1/2=e^(-k*5545)

ln(1/2)=-k*5545
-ln(2)=-k*5545
k=ln(2)/5545

0.91=e^(-ln(2)*t/5545)
ln(0.91)=-ln(2)*t/5545
t=(-ln(0.91)*5545/ln(2)

Answer 2

was this ok for you? Reply if it was, :)

Answer 3

sorry one sec

Answer 4

Yes, Thank You!