Problem 1.

Problem 1. A solution containing glucose is administered into the blood stream at a constant rate, 7'. Over time it is converted into other substances at a rate kQ where k is a positive constant and Q is the concentration of glucose. This means that the change in glucose in the bloodstream over time can be shown by the equation: dQ r a 4\" (Q r) Suppose that the rate it is administered into the body is 1 mL/s and is; has a value of 0.002 mL2 / (mg s) and t is the time measured in hours. a) Suppose that the initial concentration of the glucose is 100 mg/mL. Solve the differential equation to nd a formula for Q as a function of time. b) Suppose that the concentration at the initial time point is equal to 50 mg/mL. Use 1r'irnr'mr.ipirolframalpha.com and type in y'=-.002(y-1/0.002) , y(0) = 50 to obtain the solution of the differential equation. Sketch a graph of Q(t) below