A scientist begins with 100 mg of a radioactive substance. After 6 days, it has decayed to 60 mg. How long after the process began will it take to decay to 10 mg?

Question

Veronica Olsen

Mathematics

15 May, 12:23

A scientist begins with 100 mg of a radioactive substance. After 6 days, it has decayed to 60 mg. How long after the process began will it take to decay to 10 mg?

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Reynaldo Bryant · Answer 1

For radioactive decay:

N = N (0) x exp (-λt)

ln (6/10) = - 6λ

λ = 0.085

For the amount to become 10mg:

10 = 100exp (-0.085t)

(ln (1/10)) / - 0.085 = t

t = 27.1 days