Question: A study of British agricultural mechanization from 1950 onwards estimated that y, the number of tractors in use (measured in thousands) as a function of t (measured in years, so that t = 0 corresponds to 1950), was approximately given by y(t) = 250 + x(t), where x = x(t) satisfied the logistic differential equation
x. = 0.34x(1 - (x/230), x(0) = 25
(a) Find an expression for y(t).
(b) Find the limit of y(t) as t → ∞, and draw the graph.