Section III: Heparin 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 H, where k is a constant of proportionality, and # 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 & will be '1/hours") 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. NOTE: Only if you were unable to find a value for & in part 1, you may use k = -0.8 for the remaining questions. Otherwise, continue to use your answer from part 1. 3. Solve this differential equation to find an expression for H(t). (Note: additional writing space is available on the next page.)