The amount A of the radioactive element radium in a sample decays at a rate proportional to the amount of radium present. Given the half-life of radium is 1690 years: (a) Write a differential equation that models the amount A of radium present at time t (b) Find the general solution of the differential equation. (c) Find the particular solution of the differential equation with the initial condition A(0)=10 g. (d) How much radium will be present in the sample at t=300 years?