The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

F (t) = 361e^kt; where f (t) is the amount of radioactive material remaining after t days, k is the decay constant and t is the time elasped.

180.5 = 361e^ (32k)

e^ (32k) = 180.5/361 = 1/2

32k = ln (1/2)

k = ln (1/2) / 32

The required exponential function is f (t) = 361e^ (((ln 1/2) / 32) t)

After 5 days, f (5) = 361e^ (((ln 1/2) / 32) 5) = 323.945 kg.