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2. [Maximum marks: 8] In this question we explore radioactive decay chains. In a decay chain, atom A will decay to atom B, which then decays to atom C etc. In our case we will say that Ramanujan-1729 decays into Ramanujan-1728, which then decays into Ramanujan- 1727. (a) We start with 100 atoms of Ramanujan-1729 with a decay constant la = 1720. Ramanujan-1728 has decay constant Ab = 4104' Therefore we have the following differential equation for the rate of change of Ramanujan-1728, NB: dNB 1 dt 4104 NB + 1729 (100)e 1729 Given that when t = 0, NB = 0 Use Euler's with step size 0.1 to find an approximation for NB when t = 0.5. [6] (b) The solution to the differential equation above is given by: 100 NB (t) = 1729 1 e 1729 - e 4104t 4104 1729 Use the equation above to find NB (0.5) and comment on the accuracy of your approximation. [3] Copyright Andrew Chambers 2020. Licensed for non-commercial use only. Visit ibmathsresources.com to download the full worked mark-scheme and for 300 exploration ideas