PROBLEM 7-2

An individual drinks one carton of milk (purchased from a vending machine) daily. A problem at the dairy leads to contamination of the milk with a pesticide on three successive days. The first day, a carton of milk contains 4 mg of the pesticide, the second day 2 mg, and the third day 1 mg. (The problem is discovered and eliminated on the third day, so that there is no further contamination.) Assume the amount of pesticide in the body can adequately be modeled by assuming its rate of change is proportional to the amount.

a. Show that the amount Q(t) of the pesticide in the body at time t days following the intake of Q(0) of the pesticide is Q(0)exp(-t/T), where T is the mean residence time of the pesticide in the body.

b. Find an expression for the individual's body burden of the pesticide immediately after consuming the carton of milk on the third day of contamination.

c. Find an expression for the body burden of the pesticide for times thereafter.

d. Sketch a graph of the body burden of pesticide for one month from the time of drinking the first contaminated carton, under three different assumptions about T:

i. T = 1 (very rapid excretion or decomposition)

ii. T = 10 (intermediate)

iii. T = 100 9slow excretion or decomposition)

T = 1:

T = 10:

T= 100: