Question

Thallium-210 has a half-life of 1.32 minutes. Find an equation for the percent of Thallium-210 sample that remains after t minutes.

Answer 1

p(t) = 100%·2^(-t/1.32)

Explanation:

The equation for exponential decay is ...

(remaining amount) = (initial amount)·2^(-t/(half-life))

Here, we can represent the percentage remaining by p(t) and the initial amount by 100%. Then, for a half-life of 1.32 minutes, the amount remaining is ...

p(t) = 100%·2^(-t/1.32) . . . . . where t is in minutes

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Alternate functional forms are possible, such as ...

p(t) = 100%·e^(-0.525112t)

p(t) = 100%·0.591489^t