Question: Consider the differential equation dC/dt = 3( - C) + 1 where C is the concentration of some chemical in a cell, measured in moles

Consider the differential equation
dC/dt = 3(Г - C) + 1
where C is the concentration of some chemical in a cell, measured in moles per liter, and Г is a constant.
a. What kind of differential equation is this? Explain the terms in the equation.
b. Draw the phase-line diagram.
c. Verify the stability of the equilibrium by using the derivative.

Step by Step Solution

★★★★★

3.38 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a If is constant this is an autonomous differential equation The first term ... 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)

808-C-D-E (1228).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Consider the differential equation f + af + bf = g, where g is some fixed function. Assume that f0 is one solution of this equation, Find a solution to f + f - 6f = 2x3 - x2 - 2x.

Consider the differential equation dP/dt = f (P), where f (P) = 20.5P 3 - 1.7P + 3.4. The function f (P) has one real zero, as shown in the following figure. Without attempting to solve the...

Consider the differential equation dy/dx = e -x . (a) Explain why a solution of the DE must be an increasing function on any interval of the x- axis. (b) What are What does this suggest about a...

3) Use Equation 2.2 and then Equation 2.6 to determine the theoretical pH of a 0.1000.0005M Sodium Hydroxide (NaOH) solution Researchers have measured the electrical conductivity of ion-free (as...

Question 10 0/1 pt 0 3 98 0 Details The pl scale for acidity is defined by pl = - log,, H* ] where H|is the concentration of hydrogen ions measured in moles per liter (M). A solution has a pHI of...

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The distance that an object falls when it is dropped is directly...

Thanks in advance...detailed explanation V.2 The Blanchard OLG model for a closed economy is described by the two differential equations k = [( k) - a - (8 +g+b-m)k. ko> 0 given, (1) a = [5( in) - 8...

Answer all questions.. Part III Exercise #1. [10 pts.] A monopolist has an inverse demand curve given by p(y) = 12-y and a cost curve given by c(y) = y". Describe how to determine its...

can you help me with the processing the data part with the time given in the table Experiment 4A - lodine Clock: A Study of Reaction Rates Overview The rate at which a chemical reaction proceeds...

Can you please help me with the steps to answers the questions bellow thank you so much DETERMINATION OF THE DISSOCIATION CONSTANT OF WEAK ACIDS The acids used in parts (a) and (b) are not...

What is a job cost sheet?

Boeken testified that he read the Surgeon Generals warning about smoking in the 1960s, so how can he argue fraud?

9. Suppose the marginal benefit of writing a contract is $100, independent of its length. Find the optimal contract length when the marginal cost of writing a contract of length L is: (LO3) a. MC(L)...

Is this good market research? You and your friends are big fans of True Detective, an HBO police drama. To what extent do you think you can generalize your preference for this show to all students at...

Suppose that in Exercise 9-73, the experimenter had believed that = 14. For each of the following sample sizes, and a fixed = 0.05, find the probability of a type II error if the true mean is 205...

The marketers of shampoo products know that customers like their product to have a lot of foam. A manufacturer of shampoo claims that the foam height of his product exceeds 200 millimeters. It is...

Suppose we wish to test the hypothesis H0: = 85 versus the alternative H1: > 85 where = 16. Suppose that the true mean is = 86 and that in the practical context of the problem this is not a departure...

number 27 attached image AutoSave Off data-8_3_2021-9_06 PM - Protected View File Home Insert Draw Page Layout Formulas Data Review i PROTECTED VIEW Be careful-files from the Internet can contain...

I need help with this one. thanks! Use the following probability distribution to answer the following questions. Calculate the mean, variance, and standard deviation of the distribution. You may...

You own the following portfolio of stocks. What is the portfolio weight of stock C? 64.26 percent 58.02 percent 20.30 percent 35.74 percent 37.72 percent