Here is the question:
I have posted a link there to this thread so the OP can view my work.Mathematical modeling problem?
A 500-gal aquarium is cleansed by the recirculating filter system. Water containing impurities is pumped out at a rate of 15 gal/min, filtered, and returned to the aquarium at the same rate. Assume that passing through the filter reduces the concentration of impurities by a fractional amount a. In other words, if the impurity concentration upon entering the filter is c(t), the exit concentration is ac(t), where 0 < a < 1.
a. Apply the basic conservation principle (rate of change = rate in - rate out) to obtain a differential equation for the amount of impurities present in the aquarium at time t. Assume that filtering occurs instantaneously. If the outflow concentration at any time is c(t), assume that the inflow concentration at that same instant is ac(t).
b. What value of filtering constant a will reduce impurity levels to 1% of their original values in a period of 3 hr?