Question

There was a sample of 650 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 7.8% each year.

Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between t
and y
.

Answer 1

y = 650·0.922^t

Explanation:

At the end of each year, 92.2% of the amount at the beginning of the year remains. That is, the beginning amount is multiplied by 0.922. The exponent t in 0.922^t tells how many times (years) that multiplication has taken place. At the end of t years, the amount remaining in milligrams (y) is ...

y = 650·0.922^t