# Question #7edac

Dec 16, 2017

$6.25$ grams remaining

#### Explanation:

Use this exponential decay equation:

$y = a {\left(b\right)}^{x}$

Here $a$ is the starting amount you have, which is 100 grams in this case:

$y = 100 {\left(b\right)}^{\frac{x}{8}} \to$ You divide $x$ by $8$ because the half-life is every $8$ years

$b$ is the amount decaying each time, which is half every time:

$y = 100 {\left(\frac{1}{2}\right)}^{\frac{x}{8}}$

$x$ is the number of years, so plug in $32$ to find the remaining amount of the sample: (solve for $y$)

$y = 100 {\left(\frac{1}{2}\right)}^{\frac{32}{8}} \implies y = \text{6.25 g remaining}$