# The half-life of a certain radioactive material is 75 days. An initial amount of the material has a mass of 381 kg. How do you write an exponential function that models the decay of this material and how much radioactive material remains after 15 days?

Feb 27, 2018

Half life:

$y = x \cdot {\left(\frac{1}{2}\right)}^{t}$ with $x$ as the initial amount, $t$ as $\text{time"/"half life}$, and $y$ as the final amount. To find the answer, plug in the formula:

$y = 381 \cdot {\left(\frac{1}{2}\right)}^{\frac{15}{75}} \implies$

$y = 381 \cdot 0.87055056329 \implies$

$y = 331.679764616$

The answer is approximately $331.68$