The body regulates the level of a certain hormone. If the concentration of the hormone is above its bascline level, the liver metabolizes the hormone, reducing the excess concentration at a rate that is proportional to the excess concentration The constant of proportionality in the relationship between the elimination rate and the excess concentration is known as the velocity constant of elimination. Its value is positive and is denoted by k (measured in units of hour). Denote the excess concentration, measured in mg/L, at time t by yt) (a) Write down the right side of the differential equation satisfied by y. (Your answer should be in terms of y.) ky (Aside: Can you explain why you have a minus sign in your differential equation?) (b) Tests reveal that the velocity constant of elimination for a particular patient is 0.6 hour-1 and that their baseline hormone level is too low. A doctor tries to increase the level of hormone by giving the patient a single s a hormone supplement at time t 0. The shot causes the excess hormone concentration to immediately jump to 4.2 mg/L. He will give another shot when the hormone level falls back to 1.15 mg/L above the patient's baseline. After how long will he have to give the next shot? After 2.15887hours (c) The doctor has another patient whose baseline level is too low. He gives them a hormone supplement shot at time t-0. This causes their excess hormone concentration to immediately jump to 4 mg/L. Then level ther falls, due to the hormone being metabolized. Monitoring the excess hormone concentration, the doctor sees that the initial rate of this fall equals 0.6 mg/L/hour. What is this patient's velocity constant of elimination? 15hour- How long would it take the excess level to fall to 1.15 mg/L? 8310 、hours Another doctor has a patient whose baseline hormone level is too low. Rather than having to give a series of single shots, she decides to give the patient a continuous intravenous infusion of the hormone supplement. If there wer metabolism, the infusion would cause the concentration of hormone to increase at a constant rate of A mg L. The veloaty constant of elimination for this patient is equal to k hour-1. At the initial time, t = 0 the patient's hormon concentration is at their baseline (d) Write down the right side of the differetialeqation satisfied by y. (Your answer should be in terms of y.) dt (e) This differential equation can be rewritten in the more familiar form = k(M-y) for a particular choice of M. write down an expression for M in terms or A and k dt (t) What is the patient's initial excess hormone concentration?