Radioactive decay question
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Radioactive decay question

[From: ] [author: ] [Date: 11-10-25] [Hit: ]
ln(0.t=(-ln(0.......
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 5545 years. Suppose C(t) is the amount of carbon-14 present at time t.

(a) Find the value of the constant k in the differential equation C′=−kC.

k= ???

(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How old is the Shroud of Turin, according to these data?

Age = ??? years

-
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)
1
keywords: decay,Radioactive,question,Radioactive decay question
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