Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO).Beginning at time t = 0, cigarette smoke containing 5% CO is introduced into the room at a rateof 0.6 cubic feet per minute. The well-circulated smoke and air mixture is allowed to leave theroom at the same rate.Let A(t) represent the amount of CO in the room (in cubic feet) after t minutes.(A) Write the DE model for the time rate of change of CO in the room. Also state the initialcondition.0.6(0.05-1300)dAdtA(0)= 0(B) Solve the IVP to find the amount of CO in the room at any time t > 0.A(t) =tOF(C) Extended exposure to a CO concentration as low as 0.00012 is harmful to the human body.Find the time at which this concentration is reached.minutes=

Answered: Image /qna-images/answer/03c71b3c-0ba6-4c8e-83e8-f4486e140919.jpg

Answered: Suppose that a room containing 1300…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in hours and Ct is the concentration of caffeine. If C0 = 1000, estimate the time needed for 80% of the caffeine to be eliminated from the body (i.e. 20% left). What if C0 = 500?
Initially 53 grams of radioactive substance was present. After 6 hours the mass had decreased by 6%. If the rate of decay is proportional to the amount of the substance present at a time t, find the amount remaining after 82 hours.
A tank is filled with 200 l of salt solution containing Qo kg of salt at time t = 0. Another salt solution with 1/4 kg of salt per liter flows into the tank at a rate of 6 lt / min. By mixing, a homogeneous water-salt mixture is obtained continuously in the tank and the mixture leaves the tank at the same speed. Find the expression Q (t) which gives the amount of salt present in the tank at time t.
A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. Find the number A(t) of grams of salt in the tank at time t.
The air in a room 15 ft by 12 ft by 12 ft is 4% carbon monoxide. Starting at t = 0, fresh air containing no carbon monoxide is blown into the room at a rate of 300 ft³/min. If air in the room flows out through a vent at the same rate, when will the air in the room be 0.01% carbon monoxide? The air in the room will be 0.01% carbon monoxide after (Round to two decimal places as needed.) minutes.
At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
A tank contains 200 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
A endangered species is released into a park. The population of an endangered species is expected to follow the logistic model p(t)= 810/1+8e-188t . Where t is measured in mionths. a. How many endangered species were released into the park? b. How many endangered species will there be in 5 months? c. As time goes by, what appears to be the maximum population in the park?
A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds salt in the tank at time t.
2. Caffeine is eliminated from the body at a continuous rate of approximately 17% per hour. A standard cup of coffee contains 150mg of caffeine. a) Write a formula for the amount of caffeine C in mg as a function of the number t of hours after drinking a cup of coffee. b) Find the number of hours (to the nearest hour) it makes for half of the caffeine from a cup of coffee to be eliminated from the body. c) Find the number of hours (to the nearest hour) it takes for only 1.5mg of the caffeine from a cup of coffee to remain in the body.
Assign variables and restate the following problem in terms of known and unknown derivatives (but do not solve it): How fast is the volume of a cube increasing if its side increases at a rate of 0.5 cm/s?
A tank is initially filled with 400 gal of salt solution with a concentration of 0.08 lb/gal. At time t = 0, pure water is poured into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 3 gal/min. The tank is well-stirred. Let x(t) represent the amount of salt (in lb) in the tank after t min. Write down the initial value problem that x(t) satisfies. DO NOT SOLVE the initial value problem.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS