There's a fun piece of math you can do with this model. Given the relation w[t+1] = w[t] + (c[t] - alpha * w[t] - beta * d[t] * w[t]) / 3500 and assuming c,

There's a fun piece of math you can do with this model. Given the relation w[t+1] = w[t] + (c[t] - alpha * w[t] - beta * d[t] * w[t]) / 3500 and assuming c, d are both constant (i.e. assume they are your long-run average of calories consumed and exercise done) you can solve to get w[t] = c / (alpha + beta * d) + const * (phi ** t) where phi is a number smaller than 1, and const is some constant that depends on your initial weight. Over time, the phi t term decays away, and you are left with your long-term stable weight, w = c / (alpha + beta * d) Using c = 2000, alpha = 12.5, beta = 0.63 and d = 0 you get a long-run stable weight of w = 2000 / 12.5 = 160 lb On the other hand, if you eat 2500 calories per day but run five miles, you get w = 2500 / (12.5 + 0.63 * 5) = 160 lb so if you want to eat an extra 500 calories per day, you should run 5 miles per day. It'd be interesting to see how accurate this is.