Suppose an Infectious Disease Spreads Through an Elementary School at a Rate

True/False

Suppose an infectious disease spreads through an elementary school at a rate proportional to the product of the percentage of pupils who have the disease and the percentage of pupils who have not yet contracted the disease. Suppose that at the beginning of the epidemic 5% of the pupils have the disease. Let f(t) be the percentage of pupils who have the disease at time t; give the differential equation satisfied by f(t). Does the following accurately describe this situation: $y ^ { \prime }$ = ky(100 - y); y(0) = 0.05, where k is a positive constant?