Section III: Heparin (Section III - continued) Heparin, a blood-thinning drug, takes a relatively short time to be broken down in the human body. 1. The human body metabolizes (breaks down) heparin at a rate equal to KH, where k is a constant of proportionality, and H is the current mass of heparin in the body (H measured in mg). If the half-life of heparin in the body is 1.2 hours, what is the numerical value for the constant, k? (units of k will be '1/hours') 4. Using either the original differential equation from part 2, or the solution from part 3, find the equilibrium mass of heparin in the patient's body, reached after a long period of treatment. 2. If a patient is taking heparin at a (continuous) rate of 4 milligrams per hour, and it is being metabolized at the rate from part 1, write a differential equation that represents the net rate of change for the mass of heparin over time. 5. Consider a patient whose treatment with heparin is being halted, so that only metabolism is affecting their heparin levels . The patient currently has a level of 12 mg of heparin in their system, and a level of 0.5 mg is the lowest still considered to be clinically effective. NOTE: Only if you were unable to find a value for k in part 1, you may use k = -0.8 How long does it take after the drug supply is stopped for his or her heparin level to drop for the remaining questions. Otherwise, continue to use your answer from part 1. below the clinically effective threshold? 3. Solve this differential equation to find an expression for H(t). (Note: additional writing space is available on the next page.)