8. (8 points) You're a pharmaceutical chemist at Astra Zeneca working on the material properties of pill design. If you administer a certain pill to a patient at time t = 0, you find that the concentration of the drug in the patient's bloodstream changes at a rate of r(t) = e-0.25t - ae-0.1t where a is a constant, r(t) is measured in ng/L per hour and t is measured in hours. This model accounts both the drug entering the bloodstream due to the pill, as well as the drug leaving the bloodstream as the body metabolizes it. At t = 0, the patient had no drug in their bloodstream. (a) In plain English, interpret the meaning of / r(t) at. (b) Which of the following best represents a simplification of ("r(t) dt? O -4 (e-] - 1) + 10a(e-04 - 1) O -4 (el -1) + 10a(e-04 - 1) + C, where C is an arbitrary constant. O -4e-0.25t + 10ae-0.14 -4e-0.25t + 10ae-0.1 + C, where C is an arbitrary constant. O None of the above (c) Find the value of / r(t) dt in terms of a. "(t) at = (d) If the body eventually metabolizes all of the drug in the blood stream, what must the value of a be? Explain briefly