Question

The half-life of a certain radioactive material is 23 hours. An initial amount of the material has a mass of 82 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 7 hours.

Answer 1

Exponential decay has the form \[ P(t) = Ae^{-kt} \]Now, at time t = 0, A must be 82kg, as A is the initial amount of the radioactive material. Our equation becomes, then: \[ P(t) = 82e^{-kt} \]Now, use the half-life time definition to solve for k. Assume t in hours. Can you give it a shot?