Suppose Water Is Seeping from an Underground Storage Facility at a Rate

Multiple Choice

Suppose water is seeping from an underground storage facility at a rate that is proportional to the square amount of water present. If f(t) = y is the amount of water present at time t, find a differential equation describing the situation.

A) $y ^ { \prime }$ = $\mathrm { ky } ^ { 2 }$ , k < 0
B) $y ^ { \prime }$ = $\mathrm { ky } ^ { 2 }$ , k > 0
C) $y ^ { \prime }$ = $\mathrm { ky } ^ { 2 }$ , k < 0; y(0) =0
D) $y ^ { \prime }$ = $\mathrm { ky } ^ { 2 }$ , k > 0; y(0) = 0
E) none of these