AP Calculus question dealing with Separable Differential Equations, Please show all work. Thank you in advance :)

Free-Response Question 2 ~ with Calculator-ins points) - 2. The rate of decay is proportional to the mass for radioactive material. For a certain _ i . . - _- d ' ' ' radioactive isotope, this rate of decay is given by the differential equation run1=~.022m_,r . . , dz where m is the mass of the isotope in mg and t is the time in years. A. If m(O) = 20, write a function m(t) for the radioactive decay of the isotope. Show the 7 steps in separating variables of the given differential equation and solving the equation for m. (4 points) ' , ' B. The half-life of a radioactive substance is the time required for half of the substance to decay. What is the half-life of this radioactiVe isotope to the nearest tenth ofa year? (4 points) ' C. How many years (to the nearest tenth) will it take for the 20 mg to decay to 1 mg? (4 points) D. How many mg (to the nearest tenth) of the isotope will remain after 60 years? (3 points)