# You are given 230 grams of a substance with a half-life of 0.75 years. How much will remain after 3 years?

Feb 4, 2018

There is $\frac{1}{16}$ of the original amount, 14.375 g.

#### Explanation:

Each time a period of time goes by that is equal to the half-life, there will be only 1/2 of the previous amount of material remaining.

In this case, three years represents $3 \div 0.75 = 4$ half-lives.

So, the amount that remains has been halved four times:

$\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = {\left(\frac{1}{2}\right)}^{4} = \frac{1}{16}$

There is $\frac{1}{16}$ of the original amount, which is

$230 \times \frac{1}{16} = 14.375$ g