A stream, which is polluted with insecticide at concentration 8 g/m3 , flows at a rate of 24 m3 /day into a pond of volume 1800 m3 . At the same time, water from the pond is flowing into the sea at rate 24 m3 /day. The initial insecticide concentration in the pond is 3 g/m3 .

(a) Let y(t) be the amount of insecticide (in grams) in the pond at time t (days). Write down and solve an appropriate differential equation for y(t) along with the appropriate initial condition.

(b) After a long time, what happens to the concentration of insecticide in the pond?

(c) It is known that if the insecticide concentration in the pond reaches 7.5 g/m3 the water beetles in the pond will die. How many days does it take for the insecticide concentration to reach this threshold?