# How do you solve half life decay problems?

Jul 4, 2017

$f \left(x\right) = a \cdot {0.5}^{t / {t}_{\text{1/2}}}$

#### Explanation:

In the equation above, $a$ represents the number of starting unstable atoms, $0.5$ represents a loss of 50% of the current unstable atoms, ${t}_{\text{1/2}}$ represents a half-life time (usually in seconds, days, weeks, months or years), and $t$ represents the total time passed.

For example, $\frac{t}{t} _ \text{1/2" = "9 days"/"3 days}$ represents a 3-day half-life passing three times.