Differential Equation. Here is the entire problem below:
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 1/3500 pounds per calorie. Suppose that a particular person has a constant caloric intake of H calories per day. Let W(t) be the person's weight in pounds at time t (measured in days).
(a) What differential equation has solution W(t)? 
So I already solved for this and got that part correct. My answer was: $$\frac{dW}{dt} = \frac{1}{3500}(H-20W)$$
Below is the part that I am unsure of what to do: 
(b) If the person starts out weighing 165 pounds and consumes 3500 calories a day,$$\lim_{t\to \infty} W(t) = \text{?}$$
I at first thought to plug in the H(3500) and W(165) values that were given in the part b question into the answer I got for part A. But then I wasn't sure what to do with that answer, or if that is even the way to go. It's probably a simple solution, but I'm not seeing where to go from here. Any help would be appreciated. Thank you. 
 A: When the weight stabilizes (at infinity), the derivative cancels out and
$$H-20W_\infty=0.$$
A: We're told, 


*

*the guy needs 20 calories per day per pound of body weight to maintain his weight, and 

*he consumes 3500 clories a day. 
It follows that if he weighs $3500\div20=175$ pounds, then he will stay at 175 pounds. If he weighs any less than 175 pounds (and consumes 3500 calories per day), his weight will increase; if he weighs any more than 175 pounds, his weight will decrease. It follows that, no matter what he weighs, his weight will, in the long run, approach 175 pounds. 
Strictly speaking, there's a bit of handwaving going on here, and one ought to solve the differential equation to get a function $W(t)$, and then evaluate $\lim_{t\to\infty}W(t)$ – but at the very least the handwaving argument tells you what answer to expect. 
As for how to solve the differential equation, if your teacher really expects you to solve the differential equation, and doesn't supply you with the tools for doing so, you have a case of academic malpractice, and should go to the head of the department to inform her. But first make absolutely sure that you have not, in fact, been given the tools to solve the equation!
