Find an integrating factor for each equation. Take t > 0. y ’ – y/(10 + t) = 2
> Illustrate how the type of work that he or she does influences a person's lifestyle. For example, contrast a farmer, a factory worker, and a school teacher?
> Comment on the different dynamics of one-on-one service and group service in regard to perceived control of the service encounter.
> What are some drawbacks of increased customer participation in the service process?
> What are the organizational and marketing implications of considering a customer as a "partial employee?"
> Give an example of a service in which isolation of the technical core would be inappropriate?
> How can we design for self-recovery when self-service failures occur?
> What are the limits of the production-line approach to services?
> Conduct a triple bottom line evaluation for a hospital by identifying its social, economic, and environmental attributes that enhance the sustainability movement.
> Critique the “Distinctive Characteristics of Service Operations” by arguing that the characteristics of, customer participation, simultaneity, perishability, intangibility, and heterogeneity, may apply to goods as well.
> Compare and contrast sustainability efforts in service operations and manufacturing.
> What are challenges of the sharing economy with respect to regulation, insurance, and trust issues?
> Give examples of service firms that use the strategy of focus and differentiation and the strategy of focus and overall cost leadership.
> State the order of the differential equation and verify that the given function is a solution. (1 - t2)y’’ - 2ty ’ + 2y = 0, y(t) = t
> Answer parts (a), (b), and (c) of Exercise 9 if the person takes a 15-year fixed-rate mortgage with a 6% interest rate and intends to pay off the entire loan in 15 years. Exercise 9: The Federal Housing Finance Board reported that the national average p
> The Federal Housing Finance Board reported that the national average price of a new onefamily house in 2012 was $278,900. At the same time, the average interest rate on a conventional 30-year fixed-rate mortgage was 3.1%. A person purchased a home at the
> The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $30,303 in 2012. A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to
> A person took out a loan of $100,000 from a bank that charges 7.5% interest compounded continuously. What should be the annual rate of payments if the loan is to be paid in full in exactly 10 years? (Assume that the payments are made continuously through
> Answer the question in Exercise 5 if John contributed to his savings account at the annual rate of $3000 per year for 10 years. Exercise 5: Twenty years ahead of her retirement, Kelly opened a savings account that earns 5% interest rate compounded conti
> Twenty years ahead of her retirement, Kelly opened a savings account that earns 5% interest rate compounded continuously, and she contributed to this account at the annual rate of $1200 per year for 20 years. Ten years ahead of his retirement, John opene
> Find an integrating factor for each equation. Take t > 0. t3y ’ + y = 0
> Find an integrating factor for each equation. Take t > 0. y’ + ty = 6t
> Find an integrating factor for each equation. Take t > 0. y' - 2y = t
> Consider the initial-value problem y ’ = - y/(1 + t) + 10, y(0) = 50. (a) Is the solution increasing or decreasing when t = 0? (b) Find the solution and plot it for 0 ≤ t ≤ 4.
> A certain piece of news is being broadcast to a potential audience of 200,000 people. Let f (t) be the number of people who have heard the news after t hours. Suppose that y = f (t) satisfies y' = .07(200,000 - y), y (0) = 10. Describe this initial-va
> Solve the initial-value problem. ty’ + y = sin t, y(π/2) = 0, t > 0
> Solve the initial-value problem. y’ + 2y cos(2t) = 2 cos(2t), y(π/2) = 0
> Solve the initial-value problem. ty’ - y = -1, y(1) = 1, t > 0
> Solve the initial-value problem. y ’ + y = e2t, y(0) = -1
> Solve the initial-value problem. y’ = 2(10 - y), y(0) = 1
> Solve the initial-value problem. y ’ + y/(1 + t) = 20, y(0) = 10, t ≥ 0
> Solve the initial-value problem. ty’ + y = ln t, y(e) = 0, t > 0
> Solve the initial-value problem. y' + 2y = 1, y(0) = 1
> Solve the given equation using an integrating factor. Take t > 0. 1 / √(t + 1) y’ + y = 1
> Solve the given equation using an integrating factor. Take t > 0. y’ + y = 2 - et
> Let f (t) be the balance in a savings account at the end of t years. Suppose that y = f (t) satisfies the differential equation y’ = .04y + 2000. (a) If after 1 year the balance is $10,000, is it increasing or decreasing at that time? At what rate is it
> Solve the given equation using an integrating factor. Take t > 0. et y’ + y = 1
> Solve the given equation using an integrating factor. Take t > 0. 6y’ + ty = t
> Solve the given equation using an integrating factor. Take t > 0. y ’ = e-t (y + 1)
> Solve the given equation using an integrating factor. Take t > 0. (1 + t)y ’ + y = -1
> Solve the given equation using an integrating factor. Take t > 0. y’ - 2y = e2t
> Solve the given equation using an integrating factor. Take t > 0. y’ + y/(10 + t) = 0
> Solve the given equation using an integrating factor. Take t > 0. y’ + y = e-t + 1
> Solve the given equation using an integrating factor. Take t > 0. y’ = .5(35 - y)
> Solve the given equation using an integrating factor. Take t > 0. y ’ = 2(20 - y)
> Solve the given equation using an integrating factor. Take t > 0. y’ - 2ty = -4t
> Let f (t) be the balance in a savings account at the end of t years, and suppose that y = f (t) satisfies the differential equation y ’ = .05y - 10,000. (a) If after 1 year the balance is $150,000, is it increasing or decreasing at that time? At what rat
> Solve the given equation using an integrating factor. Take t > 0. y’ + 2ty = 0
> Solve the given equation using an integrating factor. Take t > 0. y' + y = 1
> Find an integrating factor for each equation. Take t > 0. y’ = t2(y + 1)
> Find an integrating factor for each equation. Take t > 0. y ’ + √t y = 2(t + 1)
> Solve the following differential equations: dy/dt = et/ey
> Solve the following differential equations: dy/dt = te2y
> Solve the following differential equations: dy/dt = (5 – t)/y2
> One problem in psychology is to determine the relation between some physical stimulus and the corresponding sensation or reaction produced in a subject. Suppose that, measured in appropriate units, the strength of a stimulus is s and the intensity of the
> A model that describes the relationship between the price and the weekly sales of a product might have a form such as dy/dp = -1/2 (y/p + 3), where y is the volume of sales and p is the price per unit. That is, at any time, the rate of decrease of sale
> A lake is stocked with 100 fish. Let f (t) be the number of fish after t months, and suppose that y = f (t) satisfies the differential equation y’ = .0004y(1000 - y). Figure 7 shows the graph of the solution to this differential equatio
> Solve the differential equation with the given initial condition. dN/dt = 2tN2, N(0) = 5
> Solve the differential equation with the given initial condition. dy/dx = ln x/√xy, y(1) = 4
> Solve the differential equation with the given initial condition. y ’ = t2/y , y(0) = -5
> Solve the differential equation with the given initial condition. y ’ = 5ty - 2t, y(0) = 1
> Solve the differential equation with the given initial condition. dy/dt = [(1 + t)/(1 + y)]2, y(0) = 2
> Solve the differential equation with the given initial condition. dy/dt = (t + 1)/ty, t > 0, y(1) = -3
> Solve the differential equation with the given initial condition. y' = -y2 sin t, y(π/2) = 1
> Solve the differential equation with the given initial condition. 3y2y’ = -sin t, y(π/2) = 1
> Solve the differential equation with the given initial condition. y ’ = t2 e-3y, y(0) = 2
> Solve the differential equation with the given initial condition. y2y’ = t cos t, y(0) = 2
> Let y = y(t) be the downward speed (in feet per second) of a skydiver after t seconds of free fall. This function satisfies the differential equation y ’ = .2(160 - y), y(0) = 0. What is the skydiver’s acceleration when her downward speed is 60 feet per
> Solve the differential equation with the given initial condition. y ’ = y2 - e3t y2, y(0) = 1
> Solve the differential equation with the given initial condition. y ’ = 2te-2y - e-2y, y(0) = 3
> Solve the following differential equations: yy’ = t sin(t2 + 1)
> Solve the following differential equations: y’ = (y - 3)2 ln t
> Solve the following differential equations: y2y’ = tan t
> Solve the following differential equations: y’ = ln t / ty
> Solve the following differential equations: y’ = 1/(ty + y)
> Solve the following differential equations: y ey = tet2
> Solve the following differential equations: (1 + t2) y’ = ty2
> Solve the following differential equations: y = 3t2 y2
> If the function f (t) is a solution of the initial-value problem y’ = et + y, y(0) = 0, find f (0) and f ‘ (0).
> Solve the following differential equations: y’ = (et/y)2
> Solve the following differential equations: y ’ = √(y/t)
> Solve the following differential equations: y’ = e4yt3 - e4y
> Solve the following differential equations: y ’ = (t/y)2 et3
> Solve the following differential equations: dy/dt = t2y2 / (t3 + 8)
> Solve the following differential equations: dy/dt = t1/2y2
> Solve the following differential equations: dy/dt = -1/t2y2
> Refer to the differential equation in Exercise 39. (a) Obviously, if you start with zero fish, f (t) = 0 for all t. Confirm this on the slope field. Are there any other constant solutions? (b) Describe the population of fish if the initial population is
> Let f (t) denote the number (in thousands) of fish in a lake after t years, and suppose that f (t) satisfies the differential equation y' = 0.1y (5 - y). The slope field for this equation is shown in Fig. 9. (a) With the help of the slope field, discus
> When a certain liquid substance A is heated in a flask, it decomposes into a substance B at such a rate (measured in units of A per hour) that at any time t is proportional to the square of the amount of substance A present. Let y = f (t) be the amount o
> If the function f (t) is a solution of the initial-value problem y ’ = 2y - 3, y(0) = 4, find f (0) and f ‘ (0).
> The Gompertz growth equation is dy/dt = -ay ln y/b, where a and b are positive constants. This equation is used in biology to describe the growth of certain populations. Find the general form of solutions to this differential equation. (Figure 8 shows
> Some homeowner’s insurance policies include automatic inflation coverage based on the U.S. Commerce Department’s construction cost index (CCI). Each year, the property insurance coverage is increased by an amount based on the change in the CCI. Let f (t)
> Mothballs tend to evaporate at a rate proportional to their surface area. If V is the volume of a mothball, then its surface area is roughly a constant times V2/3. So the mothball’s volume decreases at a rate proportional to V2/3. Suppose that initially
> In certain learning situations a maximum amount, M, of information can be learned, and at any time, the rate of learning is proportional to the amount yet to be learned. Let y = f (t) be the amount of information learned up to time t. Construct and solve
> Is the constant function f (t) = -4 a solution of the differential equation y’ = t2 (y + 4)?
> Is the constant function f (t) = 3 a solution of the differential equation y’ = 6 - 2y?
> State the order of the differential equation and verify that the given function is a solution. (1 - t2)y’’ - 2ty ’ + 6y = 0, y(t) = ½ (3t2 - 1)
> Let t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p(t) represent the probability that the driver will have at least one accident during these t hours. Then, 0 ≤
> Show that the function f (t) = (e-t + 1)-1 satisfies y’ + y2 = y, y(0) = ½.
> Show that the function f (t) = 5 e2t satisfies y’’ - 3y’ + 2y = 0, y(0) = 5, y’ (0) = 10.
> Show that the function f (t) = t2 – ½ is a solution of the differential equation (y’ )2 - 4y = 2.
