Linear Diet Model
Author: Segal, Arthur C.
College Mathematics Journal, Vol. 18, no. 1, pp. 44-45, 1987.
Calculus classes traditionally present a basic introduction to differential equations using examples of Newton’s law of cooling, radioactive decay, and population growth. Segal presents for consideration a simple linear model for diets, as a supplement to the standard fare. Let C be a person’s daily rate of caloric consumption, and w be the weight of that person. Using the average rate of 17.5 calories expended per pound per day, this means the average person weighing w pounds expends 17.5w calories a day. If C=17.5w then the person’s weight stays the same, and if C is higher or lower then the person gains or loses weight, respectively. How fast a person loses weight is a first order-linear equation, and it is separable if C is constant. Anxious dieters might be interested in this formula. (Summary by Ellen Le, Pomona College '10)