1 Mathematicians often study equations of the form x' (t) = rx(t)[1 – X(t)], instead of the more complicated x"(t) = cx(t)[K – X(t)), justifying the simplification with the statement that the second equation "reduces to" the first equation. Starting with y' (t) = cy(t)[K – y(t)], substitute y(t) = Kä(t) and show that the equation reduces to the form x'(t) = rx(t)[1 – x(t)]. How does the constant r relate to the constants cand K?