Question: Two chemicals A and B react to form the substance X according to the law dx /dt = k(100 - x) (50- x), where k

Two chemicals A and B react to form the substance X according to the law dx /dt = k(100 - x) (50- x), where k is a positive constant and x is the amount of substance X. Describe the amount of substance X, given the initial conditions in (a), (b), and (c). Sketch the direction field, equilibrium solutions, phase line, and solution starting from the initial value. Discuss the relative merits of each choice of initial conditions. Might a DE student question the validity of this model? Why?
(a) x(0) = 0
(b) x(0) = 75
(c) x(0) = 150

Step by Step Solution

★★★★★

3.56 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

x k 100 x 50 x The solutions for the given initial conditions are shown on the graph Note that all ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4641).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

When two chemicals, A and B, react to form another chemical C (such as in the digestive process), this is a special case of the law of mass action, which is fundamental to studying chemical reaction...

Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C....

Solve Problem 9 if 100 grams of chemical A is present initially. At what time is chemical C half formed? Data from problem 9 Two chemicals A and B are combined to form a chemical C. The rate, or...

please solve all the questions in the images! Thank you! 1. Find the particular solution to y ' = 3sin(x) given the general solution is y = C - 3cos(x) and the initial condition y(TT) = 1. (5 points)...

Application 1: The Logistic Equation Uninhibited population growth can be modeled by dp dt -= KP, k = 0 This equation is not very accurate when the population is very large. Instead, the logistic...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

The law of mass action Consider a chemical reaction k A+B a C, where A, B and C represent chemicals, A and B are the reactants, C' is the product, and k > 0 is the rate constant of the reaction. The...

I need some help on this question, I will provide the question and the article below. The law of mass action Consider a chemical reaction k A+B a C, where A, B and C represent chemicals, A and B are...

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

Solution A Solution B Kinetic Trial Deionized Water Buffer Starch 0.1 MH:0,*** 1 2 40 ml 3.0 ml 2.0 ml. 10 ml. 20 ml. 0.0 ml 5.0 ml 100 ml 100 ml 1.00 ml 100 ml 1.00 ml 1.00 ml. 100 ml 1.00 ml 0.3....

A group of statisticians at a local college has asked you to create a set of functions that compute the median and mode of a set of numbers. Define these functions in a module named stats.py. Also...

You are borrowing $725,000 to purchase a home. The mortgage will have an 8.6 % interest rate and will last for 30 years with monthly payments. How much principal and interest will you pay in the...

Mining Co. acquired mineral rights for $494,000,000. The mineral deposit is estimated at 475,000,000 tons. During the current year, 31,500,000 tons were mined and sold. What is the amount of...

(Monopoly) Suppose that a certain manufacturer has a monopoly on the sorority and fraternity ring business (a constant-cost industry) because it has persuaded the Greeks to give it exclusive rights...

Apply Theorem 5 to find the inverse A -1 of each matrix A given in Problems 3340. NOW 3-5

Apply Theorem 5 to find the inverse A -1 of each matrix A given in Problems 3340. L -4 4 3 -1 1 0 3 355 -5 -5

Apply Theorem 5 to find the inverse A -1 of each matrix A given in Problems 3340. 37 2 0 -5 -4 L 2 -1 1 32

A researcher was interested in examining the relationship between middle school students' sports activity and sex. They summarized the data they collected in a two-way table. The data collected are...

Q. 2. A winery maintains a dataset containing information about customers who subscribe to its tasting events and special offers for wine cases. The winery occasionally mails tasting to send samples...

XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 118 $ 3 2011 $ 126 $ 3 2012 $ 110 $ 3 2013 $ 115 $ 3 An investor buys six shares of...