[SOLVED] Derive the formula for the population in

> Verify that the function f (t) = 2e-t + t - 1 is a solution of the initial-value problem yâ = t - y, y(0) = 1. [This is the function shown in Fig. 4(c). In Section 10.3, you will learn how to derive this solution.] Figure 4: M co

> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not alre

> The slope field in Fig. 4(a) suggests that the solution curve of the differential equation yâ = t - y through the point (0, -1) is a straight line. (a) Assuming that this is true, find the equation of the line. (b) Verify that the funct

> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not alre

> When the breath is held, carbon dioxide (CO2) diffuses from the blood into the lungs at a steadily decreasing rate. Let P0 and Pb denote the pressure of CO2 in the lungs, respectively, in the blood at the moment when the breath is held. Suppose that Pb i

> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not alre

> Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 8; (0, 6) is on the graph; the slope is always negative, the slope becomes more negative as t increases from 0 to 3, and the slope becomes less negative as t increases from 3 to 8

> Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 7; (0, 2) is on the graph; the slope is always positive, the slope becomes more positive as t increases from 0 to 3, and the slope becomes less positive as t increases from 3 to 7

> Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 6; (0, 4) is on the graph; the slope is always negative, and the slope becomes more negative.

> Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 5; (0, 3) is on the graph; the slope is always negative, and the slope becomes less negative.

> A cool object is placed in a room that is maintained at a constant temperature of 20C. The rate at which the temperature of the object rises is proportional to the difference between the room temperature and the temperature of the object. Let y = f (t) b

> A person deposits $10,000 in a bank account and decides to make additional deposits at the rate of A dollars per year. The bank compounds interest continuously at the annual rate of 6%, and the deposits are made continuously into the account. (a) Set up

> A person planning for her retirement arranges to make continuous deposits into a savings account at the rate of $3600 per year. The savings account earns 5% interest compounded continuously. (a) Set up a differential equation that is satisfied by f (t),

> Refer to Example 2. Answer questions (a) and (b) in Exercise 1 if the interest rate is 7%. How long will it take to pay off the $25,000 loan in this case? Example 2: You took a loan of $25,000 to pay for a new car. The interest rate on the loan is 5%. Y

> Refer to Example 1. (a) How fast was the amount in the account growing when it reached $30,000? (b) How much money was in the account when it was growing at twice the rate of your annual contribution? (c) How long do you have to wait for the money in the

> A certain drug is administered intravenously to a patient at the continuous rate of r milligrams per hour. The patient’s body removes the drug from the bloodstream at a rate proportional to the amount of the drug in the blood, with constant of proportion

> Morphine is a drug that is widely used for pain management. However, morphine can cause fatal respiratory arrest. Since pain perception and drug tolerance vary with patients, morphine is gradually administered with small increments until pain is controll

> Figure 4 contains the solution of the initial-value problem in Exercise 23. Figure 4: (a) With the help of the graph, approximate how long it will take before the account is depleted. (b) Solve the initial-value problem to determine P(t). (c) Use the

> After depositing an initial amount of $10,000 in a savings account that earns 4% interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of

> You make an initial deposit of $500 in a savings account and plan on making future deposits at a gradually increasing annual rate given by 90t + 810 dollars per year, t years after the initial deposit. Assume that the deposits are made continuously and t

> A person deposits an inheritance of $100,000 in a savings account that earns 4% interest compounded continuously. This person intends to make withdrawals that will increase gradually in size with time. Suppose that the annual rate of withdrawals is 2000

> Let f (t) denote the amount of capital invested by a certain business firm at time t. The rate of change of invested capital, f ‘(t), is sometimes called the rate of net investment. The management of the firm decides that the optimum level of investment

> Radium 226 is a radioactive substance with a decay constant .00043. Suppose that radium 226 is being continuously added to an initially empty container at a constant rate of 3 milligrams per year. Let P(t) denote the number of grams of radium 226 remaini

> According to the National Kidney Foundation, in 1997 more than 260,000 Americans suffered from chronic kidney failure and needed an artificial kidney (dialysis) to stay alive. (Source: The National Kidney Foundation, www.kidney.org.) When the kidneys fai

> Find a formula for P(t) in Exercise 17 if, initially, 10,000 bacteria were present in the culture. Exercise 17: In an experiment, a certain type of bacteria was being added to a culture at the rate of e0.03t + 2 thousand bacteria per hour. Suppose that

> In an experiment, a certain type of bacteria was being added to a culture at the rate of e0.03t + 2 thousand bacteria per hour. Suppose that the bacteria grow at a rate proportional to the size of the culture at time t, with constant of proportionality k

> A body was found in a room when the room’s temperature was 70˚F. Let f (t) denote the temperature of the body t hours from the time of death. According to Newton’s law of cooling, f satisfies a differential equation of the form y = k(T - y). (a) Find

> Rework Exercise 13 for a metal with a constant of proportionality k = .2. Which rod cools faster, the rod with a constant of proportionality k = .1 or the rod with a constant of proportionality k = .2? What can you say about the effect of varying the con

> When a red-hot steel rod is plunged in a bath of water that is kept at a constant temperature 10˚C, the temperature of the rod at time t, f (t), satisfies the differential equation y = k[10 - y], where k > 0 is a constant of proportionality. Determin

> Find the demand function if the elasticity of demand is a linear function of price given by E( p) = ap + b, where a and b are constants.

> Let q = f (p) be the demand function for a certain commodity, where q is the demand quantity and p the price of 1 unit. In Section 5.3, we defined the elasticity of demand as E( p) = -p f ‘( p) / f (p). (a) Find a differential equation satisfied by th

> Let f (t) be the size of a paramecium population after t days. Suppose that y = f (t) satisfies the differential equation y’ = .003y (500 - y), y (0) = 20. Describe this initial-value problem in words.

> Find a constant solution of y’ = t2y - 5t2.

> Play Time Toys is organised into two major divisions: marketing and production. The production division is further divided into three departments: puzzles, dolls and video games. Each production department has its own manager. The companyâ&#1

> Baker Street Animal Clinic uses a particular serum routinely in its vaccination program. Veterinarian technicians give the injections. The standard dose is 10cc per injection, and the cost has been $100 per 1000cc. According to records, 2000 injections w

> The Mighty Morphs produces two popular games, Powerful Puffs and Mini-Mite Morphs. Following are standard costs: The standards call for more than one disk and documentation book per unit because of normal waste due to faulty DVDs and poor binding. Act

> Palm Producers (PP) is expecting sales growth, and so it built nearly identical automated plants in Sandy Beach, Queensland, and in Singapore to produce its new Palm Powerhouse. Each plant manager is responsible for producing adequate inventories to meet

> Your brother started a small business, GameZ, that produces a software game he developed. It is his first year in business, and he kept detailed records of the business. However, his business records consist primarily of entries in his chequebook plus in

> Northcoast Manufacturing Company, a small manufacturer of parts used in appliances, just completed its first year of operations. The companyâs controller, Vic Trainor, has been reviewing the actual results for the year and is concerned

> Security Vehicles converts Hummers into luxury, high-security vehicles by adding a computerised alarm and radar system and various luxury components. The finished vehicles are sold for $100 000 each. Variable manufacturing costs (including the cost of th

> Fighting Kites produces several different kite kits. Last year, the company produced 20Â 000 kits and sold all but 2000 kits. The kits sell for $30 each. Costs incurred are listed here. Beginning inventory last year held 2000 kits. Assume th

> Giant Jets is a French company that produces jet airplanes for commercial cargo companies. The selling price per jet is â¬1Â 000Â 000. Currently the company uses actual volumes to allocate fixed manufacturing overhea

> King Island Lobster Company is a privately held company that buys lobsters from local fishermen and then delivers them to restaurants in several of Australia’s larger cities. The owners use variable costing income statements, but one owner’s daughter, wh

> Why do the accounting standards require absorption costing for financial reporting?

> Diggers is a coal mining company. Diggers has planned to invest in replacement equipment. Its existing equipment has come to the end of its useful life and will be scrapped with no resale value. The cost of the new replacement investment is $2 500 000. I

> MacArthurâs is a fast food company planning to invest in a restaurant expansion that entails the refurbishment and opening of four new stores across the country. The cost of this investment is $4 800 000. It is to be depreciated (straig

> Lymbo Company, must install safety devices throughout its plant or it will lose its insurance coverage. Two alternatives are acceptable to the insurer. The first costs $100 000 to install and $20 000 to maintain annually. The second costs $150 000 to ins

> Ferris Industries has $50Â 000 available to invest in new equipment. Management is considering four different equipment investments, each of which requires $50Â 000. The expected after-tax cash flow for each project has been estimat

> Equipment with a cost of $60 000 will, if acquired, generate annual savings of $30 000 for six years, at which time it will have no further use or value. The company has a marginal tax rate of 40 per cent and requires a 10 per cent rate of return. It use

> Clearwater Bottling Company sells bottled spring water for $12 per case, with variable costs of $7 per case. The company has been selling 200 000 cases per year and expects to continue at that rate unless it accepts a special order from Blue Danube Resta

> Refer question 15.23 above. Outline how Ceila might improve the investment decision-making model within the hospitality and conference facilities division to cater for strategic investments. Question 15.23: FreshTucker Limited allows divisional managers

> FreshTucker Limited allows divisional managers to make capital investment decisions up to $10 million. However, divisional managers are required to send to head office details of each decision taken, including their justifications. The manager of the hos

> Amaro Hospital, a not-for-profit entity not subject to income taxes, is considering the purchase of new equipment costing $20 000 to achieve cash savings of $5000 per year in operating costs. The estimated useful life is 10 years, with no salvage value.

> Garfield Construction is considering replacing an old machine that is currently being used. The old machine is fully depreciated, but it can be used for another five years, at which time it would have no terminal value. Garfield can sell the old machine

> If inventory physically increases during the period, income under absorption costing will be higher than income using variable costing. Explain.

> Axel Ltd is planning to buy a new machine with the expectation that this investment should earn a rate of return of at least 15 per cent. This machine, which costs $150 000, would yield an estimated net cash flow of $30 000 a year for 10 years. Required

> Overnight Laundry is considering the purchase of a new pressing machine that would cost $96 000 and produce incremental operating cash flows of $25 000 annually for 10 years. The machine has a terminal value of $6000 and is depreciated for income tax pur

> Government supervisors in a remote area of Queensland are considering the purchase of a small, used plane to save on travel costs. The plane will cost $400 000 and can be sold in five years for 20 per cent of the original cost. Required If 10 per cent i

> Diamond Ltd agreed to sell some used equipment to one of its employees. Alternative financing arrangements for the sale have been discussed, and the present and future values of each alternative have been determined. Required (a) Diamond offered to acce

> (a) What is the present value of $8000 received in seven years at 8 per cent interest? (b) Bonnie Lee buys a savings bond for $125. The bond pays 6 per cent and matures in 10 years. What amount will Bonnie receive when she redeems the bond? (c) Erik Pete

> Put the following six steps for capital budgeting in the most likely order, numbering the first activity as number 1, the second as 2, and so on. • Perform sensitivity analysis. • Identify decision alternatives. • Analyse qualitative factors. • Identify

> Marissa Nafsik commenced at Mana Consulting (MANA) in 2010. The company has grown from a one-person operation to a rather diverse consulting company specialising in management consulting, technology consulting, particularly with respect to internet techn

> Maddy is the divisional manager of the internet technologies division of IT World Ltd. The following information is currently available with respect to her role. • The internet technologies division is classified as a profit centre. • Maddy reports to th

> The income statement information for Kallapur and Trombley Cotton Growers follows: Required (a) Using the general decision rule, which product should the entity emphasise? Support your answer with calculations. (b) Using the general decision rule, shou

> Horton and Associates produces two products named the Big Winner and the Loser. Last month 1000 units of the Loser and 4000 units of the Big Winner were produced and sold. Average prices and costs for the two products for last month follow: The product

> Explain how breakeven point would be affected under both absorption and variable costing.

> Feed Barn packages and distributes three grades of animal feed. The material cost per tonne and estimated annual sales for each of the products are listed. The fixed cost of operating the machinery used to package all three products is $10Â 

> Saguaro Systems produces and sells speakers and CD players. The following information has been collected about the costs related to the systems: Saguaro normally produces 25Â 000 of these systems per year. The managers have recently received

> Beautiful Biscuits (BB) sells biscuits, brownies, and beverages to small local shops. The selling price per brownie is $1.25, the variable cost is $0.75, and the average cost is $1.00. The principal of a primary school asked BB to provide 10 dozen browni

> The Cone Head House sells ice cream cones in a variety of flavours. Data for a recent week are as follows: The Cone Headâs manager received a call from a university student club requesting a bid on 100 cones to be picked up in three da

> Wildlife Foods prepares wild birdseed mixes and sells them to local pet stores, grocery stores, and wild bird stores. Two types of mixes have been most successful: Flight Fancy and Multigrain. Flight Fancy generates a contribution margin of $12 per 100 k

> Emily developed an innovative computer game, called Home By Myself (HBM). It was so successful that she quickly followed up with two sequels: Home By Myself II (HBM2) and Home By Myself III (HBM3). The costs of developing the games were $95Â 0

> The income statement for King Salmon Sales, which produces smoked salmon, follows: Assume that the administrative costs are fixed and that all of the other costs are variable. Required (a) Suppose the state government curtails fishing because of low f

> Mrs Meadows sells two popular brands of biscuits, Chip Dip and Soft Chunk Chocolate Chip. Both biscuits go through the mixing and baking departments, but Chip Dip is also dipped in chocolate in the coating department. Sales manager Frank Ronan believes t

> Snowbird Snowboards converts regular snowboards to enhance safety capabilities for children. The income statement for last year, in which 500 snowboards were produced and sold, appears here. Required (a) What volume of snowboards must be sold to earn pr

> Johnson and Sons Ltd produces organic orange juice from oranges it grows. Unfortunately, it has been a bad year for oranges because of severe frosts. Johnson only has 10 000 litres of juice. It usually sells 15 000 litres at $3 per litre. The variable co

> What is the difference between a cost that is variable and variable costing?

Question: Derive the formula for the population in