The basic equation for modelling radio-active decay is dx/dt = −rx, where x is the amount of the radio-active substance at time t, and r is the decay rate. Some radio-active substances decay into...

The basic equation for modelling radio-active decay is

dx/dt = −rx,

where x is the amount of the radio-active substance at time t, and r is the decay rate. Some radio-active substances decay into other radio-active substances, which in turn also decay. For example, Strontium 92 (r₁
= 0.256 per hr) decays into Yttrium 92 (r₂
= 0.127 per hr), which in turn decays into Zirconium. Write down a pair of differential equations for Strontium and Yttrium to describe what is happening. Starting at t = 0 with 5 × 10²⁶
atoms of Strontium 92 and none of Yttrium, use the RungeKutta formulae to solve the equations up to t = 8 hours in steps of 1/3 hr. Also use Euler’s method for the same problem, and compare your results.