Suppose someone initially weighing 180 lb adopts a diet of 2500 calories per day.
(a) Write the weight function for this individual.
(b) Graph the weight function on the window [0, 300] by [120, 200]. What is the asymptote? This value of w is the equilibrium weight w_eq. According to the model, can a person ever achieve this weight?
(c) How long will it take a dieter to reach a weight just 2 lb more than w_eq?

Exercise 51

A person’s weight depends both on the daily rate of energy consumed, say, C calories per day, and on the daily rate of energy expent, typically between 15 and 20 calories per pound per day. Using an average value of 17.5 calories per pound per day, a person weighing w pounds expends 17.5w calories per day. If C = 17.5w, then weight remains constant, and weight gain or loss occurs according to whether C is greater or less than 17.5w.

To determine how fast a change in weight will occur, the most plausible assumption is that dw/dt is proportional to the net excess (or deficit) C - 17.5w in the number of calories per day.