The half-life of a certain radioactive material is 42 days. An initial amount of the material has a mass of 49 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 8 days. Round your answer to the nearest thousandth.

The half-life of a radioactive material can be calculated by the expression:

An = Ao e^-kt

From the half-life data, we calculate the value of k.

1/2 Ao = Ao e^-k (42)

k = 0.0165

For the second conditions, we can calculate the amount remaining after 8 days.

An = 49 e^-0.0165 (8)

An = 42.9395 kg