Question

How do you determine the exponential function for a half life problem?

Answer 1

If half-life of a certain quantity `Q(t)` is `h`, then we can write

`Q(t)=Q(0)(1/2)^{t/h}`.

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Example

Suppose that a certain radioactive substance has a half-life of 20 years. If you initially have 100 g of this substance, then find the quantity function `Q(t)` of this substance after `t` years.

Since `Q(0)=100` and `h=20`, we have

`Q(t)=100(1/2)^{t/20}`.

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I hope that this was helpful.