Question

4) Frequently, a complex process can be broken down into simpler subsystems or stages that can be analyzed separately. As a simple example of this, we will break a river into 3 separate "sections" to model pollution in the system. The three sections will have volumes of V, V2, and Vs gallons of pollution. Fresh water flows into section 1, while polluted water flows from section 1 into section 2, from section 2 into section 3, and then out of section 3. Let xi(t) denote the ạmount of pollution (in pounds) in''sectioni at a time t. We will assume, for ease of the model, that each flow rate is a constant valuer dtV gallons per minute. The differential system for this model is- le-x-1-2 . Now dt V, V dt V V being good stewards of the planet, we would like to remove some of the pollution being added by the upstream humans in scction 1 in section 2 so that the amount of pollution reaching section 3 will not cause a health hazard for the humans using the section 3 water. dt V This requires the introduction of a non-homogeneity: そー" +g ( r) dt V If y-100,y-200,y-5' r-10,4(r)-100.4() -(1+С") solve the system a. of equations. b. If the initial conditions for the problem are: x,(0)-500, x2 (0) 100, (0)-10 determine the unique solutions for this problem. If the pollution in section 3 cannot go above 25 if it is to remain safe for human use, will it ever exceed that level? c. Scanned with Camscanner

Answer 1

yen, he diffestn dx, db 3 dt 0% -工ㄨㄥㄧ丟乂3 10 100, 4) are) 시。 dt 00 aoc 지(o): 5 。

200 LOO ot eeed hak level sae tos han use