When a reactor is turned off, the amount of ¹³⁵Xe decreases as it decays, but grows as ¹³⁵I decays to it. Write a pair of differential equations that describe the time rate of change of the numbers N_I and N_X of ¹³⁵I and ¹³⁵Xe nuclei respectively, and solve these equations assuming that N_I = N⁰_I and N_X = N⁰_X at t = 0. Show (using the measured half-lives of ¹³⁵I and ¹³⁵Xe) that the resulting curve of N_X(t) looks like the t > 0 section of Figure 19.5. To simplify your calculations, take N⁰_X = 0.