3. 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

An exponential function that models a radioactive decay would be written as:

An = Ao e^-kt

where An is the amount of the material left after a certain time, t. Ao is the initial amount. k is a constant.

We use the value of the half-life to find the value of k.

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

k = 0.0165

The amount remaining after 8 days is calculated as follows:

An = 49 e^ (-0.0165) (8)

An = 42.9407 kg