A radioactive element decays according to the function Q = Q0 e rt, where Q0 is

Question

A radioactive element decays according to the function Q = Q0 e rt, where Q0 is the amount of the substance at 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 isr= - 0.000139, 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. (Do not round until the final answer. Then round to the nearest year as needed.).

Explanation / Answer

Qo/2 = Qo e^(-0.000139t)

or

-0.000139t = ln(1/2)

or

t = 4986.67 years

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