For the same drug and patient as in question 1, the physician realizes that your c_eq value is too high. In fact, a concentration of 300 mg is sufficient. If we still apply a dose of b = 200 mg, what would be an appropriate time T (in hours) in between doses to achieve c_eq = 300 mg? Give your answer to one decimal place, or to the nearest minute. In between each dose the concentration will drop by a factor of a = e^-rT, before being topped up by the new dose and returning to c_eq. In addition to c_eq = 300 mg, the physician does not want the concentration to ever fall below 200 mg. Using the value of T you just derived, does the regimen in part (a) meet the physician's requirements? If not, in words what might be a way to meet these requirements? In class we derived the following general linear difference equation with constant coefficients for the concentration of a drug c_t and its change over one dosing period: c_t + 1 = ac_t + b b is the dosage amount, and a is the total decay in drug concentration in the patient's bloodstream over one dosing period. Suppose that the dosing period is fixed to be a particular amount of time, let's call it T, and also that we can write a = e^rT where r is a decay rate per unit time the depends on drug and patient. I.e. a itself declines exponentially with the interval between doses T. This just tells us that if we wait longer between doses, there will be a lower concentration at the next time interval. Derive an equilibrium solution, c_eq, in terms of b, r and T using the information above. Suppose the decay rate r = 0.2 per hour, and a convenient dose size is b = 200 mg. What is c_eq, if the dosing interval T is every 4 hours? Give your answer to the nearest mg. (Note that we are computing the total amount in the bloodstream rather than the concentration per ml.)
