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.