13. The radioactive isotope Bismuth-210 decays to Polonium-210 with half-life of 5 days. In turn, Polonium-210 decays to Lead-206 with a half-life of 138 days. Lead-206 is stable (it doesn't decay). Set up and solve a linear system of ODEs for the amount of these three elements present at time t. If you start with 100 kg of Bismuth-210 at time 0, how long does it take for half of the original mass (50 kg) to become lead?

13. The radioactive isotope Bismuth-210 decays to Polonium-210 with half-life of 5 days. In turn, Polonium-210 decays to Lead-206 with a half-life of 138 days. Lead-206 is stable (it doesn't decay). Set up and solve a linear system of ODEs for the amount of these three elements present at time t. If you start with 100 kg of Bismuth-210 at time 0, how long does it take for half of the original mass (50 kg) to become lead?