A radioactive isotope R obeys the differential equation dtdm=km, where m(t) is the mass (in milligrams) remaining t days after an experiment begins. Laboratory records show that the sample had a mass of 200\,mg at t=0 and 140\,mg exactly 5\,days later.
(a) Determine the numerical value of the constant k and include appropriate units.
(b) Using your value of k, calculate the number of days required for the sample to reach a mass of 50\,mg.