calculus

1. Seawater typically has a salinity (salt concentration) of 0.035 kg/La i.e. 35 g/L, where L denotes litre. A freshwater pond located near the sea is home to a unique ecosystem. It currently contains 60,000 L of water and has the capacity for twice that amount (Le. 120,000 L) before overowing. (Note that the pond initially contains no salt.) An unusually high tide has occurred and seawater has begun to ow into the pond at a rate of 100 L / min. This high tide will last for 10 hours. Assume the seawater immediately mixes uniformly with the pond water. Biologists are concerned about the rising salinity in the pond. As soon as the seawater starts owing in, they start draining the mixed water in the pond at a rate of 200 L / min and replacing it with fresh water (also at a rate of 200 L/ min). (a) Let -y(t) be the quantity of salt (in kg) in the pond after 15 minutes. Show that dy 2y = 3.5 . dt 600 + t For what values of t is this equation valid? (h) Solve the ODE from (a) to find -y(t) in terms of t. (c) The ecosystem may suffer severe damage if the salinity in the pond reaches 0.01 kg / L. Does this occur at the time the high tide ends