When the breath is held, carbon dioxide (CO₂) diffuses from the blood into the lungs at a steadily decreasing rate. Let P₀ and P_b denote the pressure of CO₂ in the lungs, respectively, in the blood at the moment when the breath is held. Suppose that P_b is constant during breath holding, and let P(t) denote the pressure of CO₂ in the lungs at time t > 0. Experiments show that the rate of change of P(t) is proportional to the difference between the two pressures P(t) and P_b. Find an initialvalue problem that describes the diffusion of CO₂ in the lungs during breath holding.