5. A patient initially has a concentration of 50mg/L of morphine in her blood and 70mg/L in her cerebrospinal fluid. Suppose that the drug moves into the cerebrospinal fluid at a per-capita rate of .4 and that the amount that is moved back from the cerebrospinal fluid to the bloodstream is .2 . Suppose further that the metabolism of medicine in the bloodstream is .1 and the metabolism of the drug in the cerebrospinal fluid is .2 Blood cerebrospinal fluid ( brain ) Let x(t) represent the concentration in the blood and y(t) represent the concentration in the

5. A patient initially has a concentration of 50mg/L of morphine in her blood and 70mg/L in her cerebrospinal fluid. Suppose that the drug moves into the cerebrospinal fluid at a per-capita rate of .4 and that the amount that is moved back from the cerebrospinal fluid to the bloodstream is .2 . Suppose further that the metabolism of medicine in the bloodstream is .1 and the metabolism of the drug in the cerebrospinal fluid is .2 Blood cerebrospinal fluid ( brain ) Let x(t) represent the concentration in the blood and y(t) represent the concentration in the

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

See similar textbooks

Similar questions

2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
Suppose that a healthy population of some species is growing in a limited environment and that the current population P0 is fairly close to the carrying capacity M0. You might imagine a population of fish living in a freshwater lake in a wilderness area. Suddenly a catastrophe such as the Mount St. Helens volcanic eruption contaminates the lake and destroys a significant part of the food and oxygen on which the fish depend. The result is a new environment with a carrying capacity M1 considerably less than M0 and, in fact, less than the current population P0. Starting at some time before the catastrophe, sketch a “before-and-after” curve that shows how the fish population responds to the change in environment.
It is known that in any given year, • 90% of the people in a city move to the suburbs; • 80% of the people in the suburbs do not move to the city. Given an initial city population of 55,000 and an initial suburb population of 77,000, what are the long-term population levels of the city and the suburb?
In 1969, the National Academy of Sciences published a study titled "Resources and Man." That study places "the earth's ultimate carrying capacity at about 30 billion people, at a level of chronic near-starvation for the great majority (and with massive immigration to the now less-densely populated lands)!" The study goes on to state that 10 billion people is "close to (if not above) the maximum that an intensively managed world might hope to support with some degree of comfort and individual choice." The world population in 1990 was 5.283 billion; in 2000, it was 6.082 billion. (a) Develop the mathematical model that represents world population. (Write your model in terms of t, where t is the number of years after 1990. Let p represent the world population in billions. Round the coefficient of t to seven decimal places.) p(t) = ? (b) Use the model to predict when world population would reach the "somewhat comfortable" level of 10 billion. (Round your answer to the nearest whole…
If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is would the mortality rate decrease and, if so, what percentage of deaths among hypertensives could be prevented by the education program?
Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?
1.2.3. Sociologists recognize a phenomenon called social diffusion, which is the spreading of a piece of information, a technological innovation, or a cultural fad among a population. The members of the population can be divided into two classes: those who have the information and those who do not. In a fixed population whose size is known, it is reasonable to assume that the rate of diffusion is proportional to the number who have the information times the number yet to receive it. If an denotes the number of people who have the information in a population of N people after n days, formulate a dynamical system to approximate the change in the number of people in the population who have the information.
Throughout the 20th century, a huge amount of water has been diverted from the Colorado river in the US for irrigation purposes, leaving the remaining river much higher in salinity. This water has oftenbeen saline enough that it is useless to Mexico for irrigation purposes. 49 water samples are collected salinityppm 1 148.51 2 144.91 3 144.96 4 148.55 5 145.8 6 143.84 7 146.78 8 146.11 9 146.41 10 147.21 11 145.62 12 147.75 13 145.94 14 147.1 15 148.7 16 147.31 17 145.72 18 148.81 19 148.49 20 147.55 21 146.9 22 145.08 23 149.26 24 145.14 25 150.99 26 149.62 27 145.91 28 144.24 29 144.91 30 146.94 31 145.88 32 145.67 33 144.4 34 146.31 35 144.75 36 142.9 37 145.6 38 148.33 39 145.19 40 147.68 41 143 42 146.28 43 147.49 44 147.03 45 146.62 46 145.05 47 144.62 48 144.25 49 146.65 (a) To remedy this issue, Congress has passed a law that the salinity of the Colorado river as it passes…
A manufacturing company had won a contract to supply 109200 units of a product to a customer.The production planing and control department of the company has estimated the production in the first week to be 8,000 units,but that by recruiting and training some extra staff,output will rise by 200 units each week . a. When would the company be able to complete the contract. B.If the recruitment of staff does not go as well as expected so that after six weeks ,weekly production remains constant at the level achieved in the sixth week.how long would it take to complete the contract
Two pumps capable of delivering 100 hp to an agricultural application are being evaluated in a present economy study. The selected pump will only be utilized for one year, and it will have no market value at the end of the year. Pertinent data are summarized as given follows. If electric power costs $0.10 per kWh and the pump will be operated 4,000 hours per year, which pump should be chosen? Recall that 1 hp = 0.746 kW.
A manufacturing company has been experimenting with a new additive that is used to reduce polluting effluents from its production facility. Test results suggest that if no additive is used, pollution levels are 3000 parts per million (ppm). For each pound of additive used per week, pollution levels are reduced by 0.49 ppm. The additive costs $30 per pound. The reason for experimenting with the additive is that a government agency is conducting weekly air quality tests in the vicinity of the production facility. Regulations state that if pollution levels exceed 2000 ppm, a fine is imposed. The fine is $1000 for each ppm by which the pollution level exceeds the 2000 ppm limit. If the company has budgeted $80,000 per week to spend on the additive and any pollution fines, how much additive should be purchased each week for use by the company? What is the resulting amount that the company is willing to pay in terms of weekly fines?
Suppose Tank A has 30 gallons of water containing 55 oz (ounces) of dissolved salt, Tank B has 20 gallons of water containing 26 oz of dissolved salt and Tank C has 50 gallons of water without any salt. Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min. Water flows in and out of tank A, B and C are as follows: Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min.Water flows from Tank A to Tank B at a rate of 3 gal/min.Water flows from Tank B to Tank A at a rate of 1.5 gal/min.Water flows from Tank B to Tank C at a rate of 3.5 gal/min.Water flows from Tank C to Tank B at a rate of 1 gal/min.Water drains from Tank C at a rate of 1.5 gal/min. a) Sketch the diagram that describe the above system. b) Determine the concentration of the brine inside each tank. c) Write the mathematical model that describe the above system.