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

Nov 2, 2014

If half-life of a certain quantity $Q \left(t\right)$ is $h$, then we can write

$Q \left(t\right) = Q \left(0\right) {\left(\frac{1}{2}\right)}^{\frac{t}{h}}$.

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 $Q \left(t\right)$ of this substance after $t$ years.

Since $Q \left(0\right) = 100$ and $h = 20$, we have

$Q \left(t\right) = 100 {\left(\frac{1}{2}\right)}^{\frac{t}{20}}$.

I hope that this was helpful.