# Question #076dd

May 21, 2017

$\frac{1}{8}$ of the substance will remain undecayed after 30 days.

#### Explanation:

If the half life of the substance is $10 \mathrm{da} y s$, it means that only half of the original quantity will remain at the end of $10 \mathrm{da} y s$.

So $30 \mathrm{da} y s$ is $3 \times 10 = 3 x$(half life) periods.

1) After $10 \mathrm{da} y s$ the remaining substance will be $\frac{1}{2}$

2) After $20 \mathrm{da} y s$ the remaining substance will be $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

3) After $30 \mathrm{da} y s$ the remaining substance will be $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$