The equations presented in Section 6.1 for modeling lead

The equations presented in Section 6.1 for modeling lead uptake, subsequent exchange between tissue compartments, and removal from the human body are x? 1 = (L + k12x2 + k13x3) ? (k21 + k31 + k01)x1 x? 2 = k21x1 ? (k02 + k12)x2 x? 3 = k31x1 ? k13x3. Employing the methods of Section 6.6, find the solution of this system subject to the initial conditions x1(0) = 0, x2(0) = 0, and x3(0) = 0 using the parameter values k21 = 0.011, k12 = 0.012, k31 = 0.0039, k13 = 0.000035, k01 = 0.021, k02 = 0.016, and input function L(t) = { 35, 0 ? t ? 365, 0, t > 365. Solve the problem in two stages, the first over the time interval 0 ? t ? 365 and the second over the time interval t ? 365. Evaluate the solution for the first stage at t = 365 to provide initial conditions for the second stage of the problem. You may wish to use a computer to assist your calculations. Check your results by comparing graphs of the solutions with the graphs in Figure 6.1.4 or by comparing with an approximation obtained directly by using an initial value problem solver.