Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where is a positive constant? A) ds/dt=ks - -AS (N-S) D - KS (- N)
B) ds/dt=kt ( N--t)
c) ds/dt= Ks(N--S)
d) ds/dt=KS(S--N)