Question

There was a sample of 600 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 8.4% 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

Answer: The decay rate is 8.4%, which means that the sample will have 91.6% of its original mass after one year, 91.6% of that amount after two years, and so on.

Therefore, we can write the relationship between y and t as:

y = 600 * (0.916)^t

This is an exponential decay function, where the initial value is 600 milligrams and the decay factor is 0.916 (1 minus the decay rate of 8.4%). As time t increases, the mass of the sample y decreases exponentially.

Explanation: