Chapter 1.6, Problem 45E

Let x(t) be the amount of time between two consecutive trolley cars as described above. We claim that a reasonable model for x(t) is
   $\frac{dx}{dt}=\beta x-\alpha$
Which term represents the rate of decrease of the time between the trains if no people are waiting, and which term represents the effect of the people waiting for the second train? (Justify your answer.) Should the parameters $\alpha$ and $\beta$ be positive or negative?