a lake has a receives a total input of q m3/s from a series of rivers and discharges fluid at the same rate downstream into a watershed. during the springtime the snow melts and because the river are bounded by roads there is a sudden influx of salt that is carried into the lake. once the snow melts the salt influx returns to zero. in this way, the river supplies an input of salt with concentration cin(t) = coe. the lake has a volume v and before the spring melt is relatively free of salt so that if t = 0 is the beginning of the spring melt we can consider the mass of salt in the lake to be m0 (a) write down the mathematical model for the mass m of salt in the lake use our conservation of mass developed in class (b) what is the process time constant of the lake? (c) solve the problem for the mass of salt and assume i. k q/v. do not complete the 7th step where we sketch m(t). ii. assume that k = v/q. complete the 7th step and sketch m(t). iii. find the limit as k → q/v in 6(c), and show that you recover 6(c)ii. you may use l'hopital's rule or just set q/v - k+e and approximate for small e you'll need fact that eanythingsmall 1 + anythingsmall