Suppose That a Substance a Is Converted to Substance B $y ^ { \prime }$

Multiple Choice

Suppose that a substance A is converted to substance B at a rate that is proportional to the cube of the amount of B present. The amount of A and B together is always constant, say M. If f( t) = y is the amount of A present at time t, then which of the following differential equation describes the situation?

A) $y ^ { \prime }$ = $k ( M - y ) ^ { 3 }$ ; k < 0
B) $y ^ { \prime }$ = $k ( M - y ) ^ { 3 }$ ; k > 0
C) $y ^ { \prime }$ = $\mathrm { ky } ^ { 3 }$ ; k > 0
D) $y ^ { \prime }$ = $\mathrm { ky } ^ { 3 }$ ; k < 0
E) none of these