This question is for a 100 level college course about programming in MATLAB only.

The basic equation for modeling radioactive decay is

dx/dt = - rx

where x is the amount of radioactive substance at time t and r is the decay rate. Some radioactive substances decay into other radioactive substances, which in turn also decay. For example, Strontium 92 (r₁= 0.256/hour) decays into Yttrium 92 (r₂ = 0.127/hour) which in turn decays into Zirconium. Write down a pair of equations for Strontium and Yttrium to describe what is happening. Starting at t = 0 with 5 x 10²⁶ atoms of Strontium 92 and none of Yttrium, use the Euler method to solve the equations up to t = 8 hours in steps of 1/3 hour. Also use the Runge-Kutta (ode23) method for the same problem and compare your results. Clearly explain your method of solution, with sample input and output and any tests that you do to make sure the programs work correctly.