How is exponential decay related to a half-life?

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How is exponential decay related to a half-life?

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Answer 1 · 2018-05-05T04:18:02

Half-life is a form of exponential decay over time.
See below.

Explanation:

Assume you have an initial quantity ( $Q_{0}$ $Q_0$ ) of a substance with a half-life period of $h$ $h$ , then after $t$ $t$ time periods the quantity remaining ( $Q_{t}$ $Q_t$ ) will be given by:

$Q_{t} = Q_{0} \cdot {(\frac{1}{2})}^{\frac{t}{h}}$ $Q_t = Q_0*(1/2)^(t/h)$

This means that the quantity will halve in value after $h$ $h$ time periods.

An example:

The half-life of Plutonium-241 is 14.4 years. If I start with 1000 gm after 5 years and 50 years I will have:

$Q_{5} = 1000 \cdot {(\frac{1}{2})}^{\frac{5}{14.4}} \approx 786.1$ $Q_5 = 1000 * (1/2)^(5/14.4) approx 786.1$ gm

$Q_{50} = 1000 \cdot {(\frac{1}{2})}^{\frac{50}{14.4}} \approx 90.1$ $Q_50 = 1000 *(1/2)^(50/14.4) approx 90.1$ gm

This is a form of exponential decay.

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How is exponential decay related to a half-life?

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