This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 6 Due Monday February 14th, 2011 (1) A lake, with volume V = 100 km 3 , is fed by a river at a rate of r km 3 / yr. In addition, there is a factory on the lake that introduces a pollutant into the lake at the rate of p km 3 / yr. There is another river that is fed by the lake at a rate that keeps the volume of the lake constant. This means that the rate of flow from the lake into the outlet river is ( p + r ) km 3 / yr. Let x ( t ) denote the volume of the pollutant in the lake at time t . Then c ( t ) = x ( t ) /V is the concentration of the pollutant. (a) Show that, under the assumption of immediate and perfect mixing of the pollutant into the lake water, the concenetration satisfies the differential equation c + p + r V c = p V . (b) It has been determined that a concentration of over 2% is hazardous for the fish in the lake. Suppose that r = 50 km 3 / yr, p = 2 km 3 / yr, and the initial concentration of pollutant in the lake is zero. How long will it take the lake to become hazardousof pollutant in the lake is zero....
View Full Document