Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Chapter 9.6, Problem 8E
To determine
To use:
The graphs of populations to sketch the corresponding phase trajectory.
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CS21.pdf
1
- 3
2.
Consider a model with an interaction term between being female and being married. The dependent variable is the log of the
hourly wage:
log(wage) = 0.151 - 0.038 female + 0.1 married - 0.301 female* married + 0.079 educ + 0.027 exper+0.029 tenure
(0.072)
(0.056)
(0.055)
(0.007)
(0.005)
(0.007)
n = 536, R2 = 0.461
Numbers in parantheses are standard errors of coefficients. Given the estimation result and the observation number fill in the
blanks below which aim at discussing the statistical significance of variables.
The test statistic of the interaction term is
The critical value at 1% significance level is
Then the interaction term
statistically significant at 1% significance level. (Hint: to fill the blank
make a choice between "is" and "is not".)
The longitude, rt of an air plane is affected by a random component e, due to the
wind effect and its speed t
It = -1 + 20t-1 + 6t.
The speed of the plane is affected by a constant global linear trend, ß = B₁-1 = 3, and varies
randomly due to weather conditions,
v₁ = V₁-1 + B₁-1+w₂.
In the above equations, is assumed to be white Gaussian noise with zero mean and o = 3.
Similarly w is assumed to be white Gaussian noise with zero mean and 2,=0.5. A GPS transmitter
mounted on the plane sends a noisy measurement to a receiver about its position,
X₁ = 0.5xt + nt,
where n, is assumed to be white Gaussian noise with zero mean and o2 = 2.
(a) Using the following definition for the state vector, 0t.
0₁
It + ve
B₂
write the motion of the plane in state space form. Note: You need to provide the exact form
of the h, G and W matrices.
(b) Evaluate the initial estimate for the state vector 03-
Chapter 9 Solutions
Calculus (MindTap Course List)
Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Verify that y=tcostt is a solution of the...Ch. 9.1 - a For what values of r does the function y=erx...Ch. 9.1 - Prob. 4ECh. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - a Show that every member of the family of...Ch. 9.1 - a What can you say about a solution of the...Ch. 9.1 - a What can you say about the graph of a solution...Ch. 9.1 - Prob. 9ECh. 9.1 - The Fitzhugh-Nagumo model for the electrical...
Ch. 9.1 - Explain why the functions with the given graphs...Ch. 9.1 - The function with the given graph is a solution of...Ch. 9.1 - Match the differential equations with the solution...Ch. 9.1 - Suppose you have just poured a cup of freshly...Ch. 9.1 - Prob. 15ECh. 9.1 - Von Bertalanffys equation states that the rate of...Ch. 9.1 - Differential equations have been used extensively...Ch. 9.2 - A direction field for the differential equation...Ch. 9.2 - A direction field for the differential equation...Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - 910 Sketch a direction field for the differential...Ch. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Use a computer algebra system to draw a direction...Ch. 9.2 - Make a rough sketch of a direction field for the...Ch. 9.2 - a Use Eulers method with each of the following...Ch. 9.2 - A direction field for a differential equation is...Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Use Eulers method with step size 0.1 to estimate...Ch. 9.2 - Prob. 24ECh. 9.2 - a Program a calculator or computer to use Eulers...Ch. 9.2 - a Program your computer algebra system, using...Ch. 9.2 - The figure shows a circuit containing an...Ch. 9.2 - In Exercise 9.1.14 we considered a 95C cup of...Ch. 9.3 - 110 Solve the differential equation. dydx=3x2y2Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - 110 Solve the differential equation. y+xey=0Ch. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Find an equation of the curve that passes through...Ch. 9.3 - Find the function f such that...Ch. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - a Use a computer algebra system to draw a...Ch. 9.3 - 2728 a Use a computer algebra system to draw a...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 3335 An integral equation is an equation that...Ch. 9.3 - 3335 An integral equation is an equation that...Ch. 9.3 - Prob. 35ECh. 9.3 - Find a function f such that f(3)=2 and...Ch. 9.3 - Prob. 37ECh. 9.3 - In Exercise 9.2.28 we discussed a differential...Ch. 9.3 - Prob. 39ECh. 9.3 - In an elementary chemical reaction, single...Ch. 9.3 - In contrast to the situation of Exercise 40,...Ch. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - A certain small country has 10 billion in paper...Ch. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - A vat with 500 gallons of beer contains 4 alcohol...Ch. 9.3 - A tank contains 1000 L of pure water. Brine that...Ch. 9.3 - Prob. 49ECh. 9.3 - An object of mass m is moving horizontally through...Ch. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Let A(t) be the area of a tissue culture at time t...Ch. 9.3 - Prob. 54ECh. 9.4 - 12 A population grows according to the given...Ch. 9.4 - 1-2 A population grows according to the given...Ch. 9.4 - Suppose that a population develops according to...Ch. 9.4 - Suppose that a population grows according to a...Ch. 9.4 - The Pacific halibut fishery has been modeled by...Ch. 9.4 - Suppose a population P(t) satisfies...Ch. 9.4 - Suppose a population grows according to a logistic...Ch. 9.4 - The table gives the number of yeast cells in a new...Ch. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - One model for the spread of a rumor is that the...Ch. 9.4 - Biologists stocked a lake with 400 fish and...Ch. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Consider a population P=P(t) with constant...Ch. 9.4 - Let c be a positive number. A differential...Ch. 9.4 - Lets modify the logistic differential equation of...Ch. 9.4 - Consider the differential equation...Ch. 9.4 - There is considerable evidence to support the...Ch. 9.4 - Prob. 22ECh. 9.4 - In a seasonal-growth model, a periodic function of...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - 514 Solve the differential equation. y+y=1Ch. 9.5 - 514 Solve the differential equation. yy=exCh. 9.5 - 514 Solve the differential equation. y=xyCh. 9.5 - 514 Solve the differential equation....Ch. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - A Bernoulli differential equation named after...Ch. 9.5 - 2425 Use the method of Exercise 23 to solve the...Ch. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - In Section 9.3 we looked at mixing problems in...Ch. 9.5 - Prob. 34ECh. 9.5 - An object with mass m is dropped from rest and we...Ch. 9.5 - If we ignore air resistance, we can conclude that...Ch. 9.5 - Prob. 37ECh. 9.5 - To account for seasonal variation in the logistic...Ch. 9.6 - For each predator-prey system, determine which of...Ch. 9.6 - Each system of differential equations is a model...Ch. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 78 Graphs of populations of two species are shown....Ch. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Populations of aphids and ladybugs are modeled by...Ch. 9.6 - In Example 1 we used Lotka-Volterra equations to...Ch. 9.6 - In Exercise 10 we modeled populations of aphids...Ch. 9.R - Prob. 1CCCh. 9.R - Prob. 2CCCh. 9.R - Prob. 3CCCh. 9.R - Prob. 4CCCh. 9.R - Prob. 5CCCh. 9.R - Prob. 6CCCh. 9.R - Prob. 7CCCh. 9.R - Prob. 8CCCh. 9.R - a Write Lotka-Volterra equations to model...Ch. 9.R - Prob. 1TFQCh. 9.R - Prob. 2TFQCh. 9.R - Prob. 3TFQCh. 9.R - Determine whether the statement is true or false....Ch. 9.R - Prob. 5TFQCh. 9.R - Determine whether the statement is true or false....Ch. 9.R - Prob. 7TFQCh. 9.R - Prob. 1ECh. 9.R - a Sketch a direction field for the differential...Ch. 9.R - a A direction field for the differential equation...Ch. 9.R - Prob. 4ECh. 9.R - Prob. 5ECh. 9.R - Prob. 6ECh. 9.R - 58 Solve the differential equation. 2yey2y=2x+3xCh. 9.R - 58 Solve the differential equation. x2yy=2x3e1/xCh. 9.R - 911 Solve the initial-value problem....Ch. 9.R - 911 Solve the initial-value problem....Ch. 9.R - Prob. 11ECh. 9.R - Prob. 12ECh. 9.R - 1314 Find the orthogonal trajectories of the...Ch. 9.R - Prob. 14ECh. 9.R - Prob. 15ECh. 9.R - a The population of the world was 6.1 billion in...Ch. 9.R - Prob. 17ECh. 9.R - Prob. 18ECh. 9.R - One model for the spread of an epidemic is that...Ch. 9.R - Prob. 20ECh. 9.R - Prob. 21ECh. 9.R - Populations of birds and insects are modeled by...Ch. 9.R - Prob. 23ECh. 9.R - Prob. 24ECh. 9.P - Find all functions f such that f is continuous and...Ch. 9.P - Prob. 2PCh. 9.P - Prob. 3PCh. 9.P - Find all functions f that satisfy the equation...Ch. 9.P - Prob. 5PCh. 9.P - A subtangent is a portion of the x-axis that lies...Ch. 9.P - A peach pie is taken out of the oven at 5:00 PM....Ch. 9.P - Snow began to fall during the morning of February...Ch. 9.P - A dog sees a rabbit running in a straight line...Ch. 9.P - a Suppose that the dog in Problem 9 runs twice as...Ch. 9.P - A planning engineer for a new alum plant must...Ch. 9.P - Prob. 12PCh. 9.P - Prob. 13PCh. 9.P - Prob. 14PCh. 9.P - Prob. 15PCh. 9.P - a An outfielder fields a baseball 280 ft away from...
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