1. 13 marks A stream, which is polluted with insecticide at concentration 7 g/m°, flows at a rate of 20 m/day into a pond of volume 1500 m³. At the

same time, water from the pond is flowing into the sea at rate 20 m³/day. The initial insecticide concentration in the pond is 4 g/m'3³. (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 6 g/m water beetles in the pond will die. How many days does it take for the insecticide the concentration to reach this threshold?