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?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdea9377e-54a6-4732-b70e-605d87d37d77%2F5fbb02e8-c278-4631-98e7-5396a164e89c%2Fg598x0h_processed.png&w=3840&q=75)
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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