The rate of radioactive decay of a mass of Radium -226 (call it dm/dt) is proportional to the amount m of Radium present at time t. Suppose we begin with 100 milligrams of Radium at time t = 0.
(a) Given that the half life of Radium-226 is roughly 1600 years (half life is the time it takes for the mass to decay by half), find a formula for the mass of Radium that remains after t years by solving a differential equation.
(b) Find the amount of Radium remaining after 1000 years. Simplify your answer using the fact that 2-10/16 ≈ 65.