Simple physiological model

According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is pounds per calorie. Suppose that a particular person has a constant caloric intake of calories per day. Let be the person’s weight in pounds at time (measured in days).

(a) What differential equation has solution ?

(Your answer may involve W, H and values given in the problem.)

(b) Solve this differential equation, if the person starts out weighing 175 pounds and consumes 3300 calories a day.

(c) What happens to the person’s weight as ?

Sample Solution