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Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams) of pollutant, evenly distributed throughout the lake with a concentration q(t) (grams per gallon), where q(t) = Q(t)/V. Assume that water containing a concentration k (gram per gallon) of pollutant enters the lake at a rate r (gallons per week), and that water leaves the lake at the same rate. Suppose that pollutants are also added directly to the lake at a constant rate P (grams per week) from a location of a lake different than the inflow or outflow of water. (a) ,. the lake over time. -) Write a differential equation that models the change in the amount of pollutant Q in -) If at time t = 0 the concentration of pollutant is qo, find an expression for the (b) concentration q(t) at any time. ) What is the limiting (i.e. highest) concentration as t → oo?

Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams) of pollutant, evenly distributed throughout the lake with a concentration q(t) (grams per gallon), where q(t) = Q(t)/V. Assume that water containing a concentration k (gram per gallon) of pollutant enters the lake at a rate r (gallons per week), and that water leaves the lake at the same rate. Suppose that pollutants are also added directly to the lake at a constant rate P (grams per week) from a location of a lake different than the inflow or outflow of water. (a) ,. the lake over time. -) Write a differential equation that models the change in the amount of pollutant Q in -) If at time t = 0 the concentration of pollutant is qo, find an expression for the (b) concentration q(t) at any time. ) What is the limiting (i.e. highest) concentration as t → oo?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams) of pollutant, evenly distributed throughout the lake with a concentration q(t) (grams per gallon), where q(t) = Q(t)/V. Assume that water containing a concentration k (gram per gallon) of pollutant enters the lake at a rate r (gallons per week), and that water leaves the lake at the same rate. Suppose that pollutants are also added directly to the lake at a constant rate P (grams per week) from a location of a lake different than the inflow or outflow of water. (a) ,. the lake over time. ) Write a differential equation that models the change in the amount of pollutant Q in -) If at time t = 0 the concentration of pollutant is qo, find an expression for the (b) concentration q(t) at any time. (c) (d) determine the time interval T that must elapse before the concentration of pollutants is reduced to 10% of its original value. ) What is the limiting (i.e. highest) concentration as t → oo? If the addition of pollutants to the lake is terminated (k = 0 and P = 0 for t > 0),
Transcribed Image Text:Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams) of pollutant, evenly distributed throughout the lake with a concentration q(t) (grams per gallon), where q(t) = Q(t)/V. Assume that water containing a concentration k (gram per gallon) of pollutant enters the lake at a rate r (gallons per week), and that water leaves the lake at the same rate. Suppose that pollutants are also added directly to the lake at a constant rate P (grams per week) from a location of a lake different than the inflow or outflow of water. (a) ,. the lake over time. ) Write a differential equation that models the change in the amount of pollutant Q in -) If at time t = 0 the concentration of pollutant is qo, find an expression for the (b) concentration q(t) at any time. (c) (d) determine the time interval T that must elapse before the concentration of pollutants is reduced to 10% of its original value. ) What is the limiting (i.e. highest) concentration as t → oo? If the addition of pollutants to the lake is terminated (k = 0 and P = 0 for t > 0),
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