Assignment:
A polluted river with a nutrient concentration of 110g/m^3 is flowing at a rate of 130m^3/day into an estuary of volume 1000m^3. At the same time, water from the estruary is flowing into the ocean at 120m^3/day. The initial nutrient concentration in the estuary is 35g/m^3.
(i) Let N(t) be the amount of nutrient (in grams) in the estuary at time t. Write down and solve and solve an appropriate differential equation for N(t) along with the appropriate initial condition.
(ii) After a long time, what is the concentration of nutrient in the estuary?
(iii) It is known that if the nutrient concentration in the estuary reaches 85g/m^3 an algal bloom will occur. How many days does it take for the nutrient concentration to reach this threshold?
Provide complete and step by step solution for the question and show calculations and use formulas.