jainybrother-1

5. The body regulates the level of a certain hormone. If the concentration of the hor mone is above baseline level, the liver metabolizes the hormone, reducing the excess concentration at a rate that is proportional to the excess concentration. The constant elimination rate and the excess con- centration is known as the velocity constant of elimination. Its value is positive and is denoted by k, measured in hours-1. Denote the excess concentration, measured in of proportionality in the relationship between the mg/L, at time t in hours by y(t). (a) Write down the differential equation satisfied by y(t). (Make sure to think about whether dy/dt should be positive or negative, and reflect that in your equation.) (b) A doctor has a patient whose baseline level of the hormone is too low. She will give her patient a hormone supplement shot that causes the patient's excess hormone concentration to immediately jump to 4 mg/L. Then the hormone level falls due to the hormone being metabolized. When the doctor monitors the patient's excess hormone concentration, she finds that the initial rate of the fall in concentration is 1.05 (mg/L)/hour. Once the excess hormone level falls to 0.6 mg/L above the patient's baseline level, the doctor will give another hormone shot. At what time will this occur?