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.

Question

Mathematics

Glenn Barker

10 December, 12:24

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.

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Answers (1)

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Campbell Russell · Answer 1

y = 350 (0.943) t

Step-by-step 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