Biological Half-Life Problem: While working, you accidentally inhale some mildly

Chapter 7, Problem 5

(choose chapter or problem)

Biological Half-Life Problem: While working, you accidentally inhale some mildly poisonous fumes. Twenty hours later you still feel a bit woozy, so you finally report to the medical facility where you are sent by your employer. From blood samples, the doctor measures a poison concentration of 0.00372 mg/mL and tells you to come back in 8 hours. On the second visit, she measures a concentration of 0.00219 mg/mL. Let t be the number of hours that have elapsed since you first visited the doctor and let C be the concentration of poison in your blood, in milligrams per milliliter. From biology, you realize that the instantaneous rate of change of C with respect to t is directly proportional to C. a. Write a differential equation that relates these two variables. b. Solve the differential equation subject to the initial conditions specified. Express C as a function of t. c. The doctor says that you could have suffered serious damage if the concentration of poison had ever been 0.015 mg/mL. Based on your mathematical model from part a, was the concentration ever that high? Justify your answer. d. Plot the graph of this function. Sketch the function, showing the values in part c. e. The biological half-life of a poison is thelength of time it takes for its concentrationto drop to half of its present value. Find thebiological half-life of this poison.