A laboratory stores a 150\,mg sample of the radioactive isotope cesium\textendash137. The mass M(t) (in milligrams) present t years after storage satisfies dtdM=kM.
(a) Calculate the decay constant k for cesium\textendash137, given that its half\textendash life is 30.17\,years. Express your answer exactly.
(b) Determine the least integer number of years required for the mass of the sample to fall below 40\,mg. Provide both an exact expression and a decimal approximation correct to the nearest tenth of a year.