Question

There was a sample of 350 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 5.7% 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 y and t.

Answer 1

y = 350(0.943)t

Explanation:

Mass of sample after t years is given by

y = Initial mass * (1 - r)t

In this case,

Initial mass = 350 mg

r = 5.7% = 0.057

Therefore,

y = 350(1 - 0.057)t

=> y = 350(0.943)t

Therefore, relationship between y and t is given by

y = 350(0.943)t