Let T Represent the Number of Hours That a Packing $y ^ { \prime }$

Multiple Choice

Let t represent the number of hours that a packing machine is operated and y(t) represent the probability that the machine breaks down at least once during the t hours of operation. It has been observed that the rate of increase of the probability of a breakdown is proportional to the probability of not having a breakdown. Find a differential equation describing this situation.

A) $y ^ { \prime }$ = ky; There is not enough information given to determine initial conditions.
B) $y ^ { \prime }$ = ky; y(0) = 0
C) $y ^ { \prime }$ = k(1 - y) ; There is not enough information given to determine initial conditions.
D) $y ^ { \prime }$ = k(1 - y) ; y(0) = 0
E) $y ^ { \prime }$ = (1 + y) ; y(0) =0