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4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration tons/km³. y(t) 12200 Assume that fresh water enters the lake at a rate of 67.1 km³/yr, and that water leaves the lake at the same rate. Suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr. Among the many simplifying assumptions that must be made to model such a complicated real-world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake. A. Write a differential equation for y(t). B. Solve the differential equation for initial condition y(0) = 200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as t goes from 0 to infinity.

4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration tons/km³. y(t) 12200 Assume that fresh water enters the lake at a rate of 67.1 km³/yr, and that water leaves the lake at the same rate. Suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr. Among the many simplifying assumptions that must be made to model such a complicated real-world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake. A. Write a differential equation for y(t). B. Solve the differential equation for initial condition y(0) = 200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as t goes from 0 to infinity.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Consider a lake of constant volume 12200 km³, which at time i contains an amount y(t) tons of y(t) pollutant evenly distributed throughout the lake with a concentration - tons/km³. 12200 Assume that fresh water enters the lake at a rate of 67.1 km³/yr, and that water leaves the lake at the same rate. Suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr. Among the many simplifying assumptions that must be made to model such a complicated real-world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake. A. Write a differential equation for y(t). B. Solve the differential equation for initial condition y(0) = 200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as t goes from 0 to infinity.
Transcribed Image Text:4. Consider a lake of constant volume 12200 km³, which at time i contains an amount y(t) tons of y(t) pollutant evenly distributed throughout the lake with a concentration - tons/km³. 12200 Assume that fresh water enters the lake at a rate of 67.1 km³/yr, and that water leaves the lake at the same rate. Suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr. Among the many simplifying assumptions that must be made to model such a complicated real-world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake. A. Write a differential equation for y(t). B. Solve the differential equation for initial condition y(0) = 200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as t goes from 0 to infinity.
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