A radioactive element decays according to the function Q=Q 0 e rt , where Q 0 is

Question

A radioactive element decays according to the function Q=Q0 ert, where Q0 is the amount of substancee at the time t=0, r is the continuous compound rate of decay, t is the time in years, and Q is the amount of the substance at time t. If the continuous compound rate of the element per year is r=-0.000386 , how long will it take a certain amount of this element to decay to half the original amount?

(The period is the half-life of the substance.) The half-life of the element is approximately _____years.

Explanation / Answer

Q=Q0ert

Half of origional value means Q=Q0/2

Q0/2=Q0e-0.000386t

1/2=e-0.000386t

ln(1/2)=-0.000386t

t=approx 1796 years

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