Question

The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 18 hours. Round your answer to the nearest thousandth.

Answer 1

Write an exponential function that models the decay of this material.

The function is described by the half-life equation which is expressed as:

An = Ao e^-kt where An is the amount left after t time, Ao is the initial amount and k is a constant.

Find how much radioactive material remains after 18 hours. Round your answer to the nearest thousandth.

1/2Ao = Ao e^-k(78)
k = 8.89 x 10^-3

An = 790e^-8.89 x 10^-3(18)
An = 673.22 kg