The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days.
Round your answer to the nearest thousandth.

Question

The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days.
 Round your answer to the nearest thousandth.

kainui · Answer

What is the standard formula for an exponential decay?$$P =P _{o}e^{-kt}$$Now how do you know the rate if you just know the half life? Well, half-life is just the amount of time it takes for the total amount of your original substance to decay by half. So we can say $$(1/2)P _{o}=P _{o}e^{-kt _{1/2}}$$with a little bit of algebra you'll see the relationship between rate and half-life!