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A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day into a pond of volume 1800 m³. At the same time, water from the pond is flowing into the sea at rate 24 m/day. The initial insecticide concentration in the pond is 3 g/m³. (a) Let y(t) be the amount of insecticide (in grams) in the pond at time t (days). Write down and solve an appropriate differential equation for y(t) along with the appropriate initial condition. (b) After a long time, what happens to the concentration of insecticide in the pond? (c) It is known that if the insecticide concentration in the pond reaches 7.5 g/m³ the water beetles in the pond will die. How many days does it take for the insecticide concentration to reach this threshold?

A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day into a pond of volume 1800 m³. At the same time, water from the pond is flowing into the sea at rate 24 m/day. The initial insecticide concentration in the pond is 3 g/m³. (a) Let y(t) be the amount of insecticide (in grams) in the pond at time t (days). Write down and solve an appropriate differential equation for y(t) along with the appropriate initial condition. (b) After a long time, what happens to the concentration of insecticide in the pond? (c) It is known that if the insecticide concentration in the pond reaches 7.5 g/m³ the water beetles in the pond will die. How many days does it take for the insecticide concentration to reach this threshold?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day into a pond of volume 1800 m³. At the same time, water from the pond is flowing into the sea at rate 24 m/day. The initial insecticide concentration in the pond is 3 g/m³. (a) Let y(t) be the amount of insecticide (in grams) in the pond at time t (days). Write down and solve an appropriate differential equation for y(t) along with the appropriate initial condition. (b) After a long time, what happens to the concentration of insecticide in the pond? (c) It is known that if the insecticide concentration in the pond reaches 7.5 g/m³ the water beetles in the pond will die. How many days does it take for the insecticide concentration to reach this threshold?
Transcribed Image Text:A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day into a pond of volume 1800 m³. At the same time, water from the pond is flowing into the sea at rate 24 m/day. The initial insecticide concentration in the pond is 3 g/m³. (a) Let y(t) be the amount of insecticide (in grams) in the pond at time t (days). Write down and solve an appropriate differential equation for y(t) along with the appropriate initial condition. (b) After a long time, what happens to the concentration of insecticide in the pond? (c) It is known that if the insecticide concentration in the pond reaches 7.5 g/m³ the water beetles in the pond will die. How many days does it take for the insecticide concentration to reach this threshold?
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