In a certain chemical reaction, substance A combines with substance B to form substance Y. At the start of the reaction, the quantity of A present is a grams and the quantity of B present is b grams. Assume a < b and y a. At time t seconds after the start of the reaction, the quantity of Y present is y grams. For certain types of reactions, the rate of the reaction, in grams/sec, is given by
Rate = k(a - y)(b - y),
where k is a positive constant.
1. Sketch a graph of the rate against y. For what values of y is the rate nonnegative? Give your answer as a union of intervals, e.g, (-infinity-a] U (a, 2b) 2.
y ∊ _____
