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 m³/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 m³/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?
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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Hello please see the attached image
![A stream, which is polluted with insecticide at concentration 8 g/m³, flows at
a rate of 24 m /day into a pond of volume 1800 m³. At the same time, water from the
pond is flowing into the sea at rate 24 m³/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%2Fa3fe4686-b98e-4efa-ab6b-44e2e8381ba5%2F5489b72e-03a2-4375-ad32-208712972997%2Fpexvj3k_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 m /day into a pond of volume 1800 m³. At the same time, water from the
pond is flowing into the sea at rate 24 m³/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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