CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.3, Problem 44E
A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country’s banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let x = x(t) denote the amount of new currency in circulation at time t with x(0) = 0.
- (a) Formulate a mathematical model in the form of an initial- value problem that represents the “flow” of the new currency into circulation.
- (b) Solve the initial-value problem found in part (a).
- (c) How long will it take for the new bills to account for 90% of the currency in circulation?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
An investor is presented with a choice of two investments: an established furniture store and
a new book store. Each choice requires the same initial investment and each produces a
continuous income stream of 6%, compounded continuously. The rate of flow of income
from the furniture store is f(t)= 18,000, and the rate of flow of income from the book store is
expected to be g(t) = 16,000e0.03t Compare the future values of these investments to
determine which is the better choice over the next 8 years.
The future value of the furniture store is $
(Round to the nearest dollar as needed.)
www
2) The Nikkei 225 index is a stock market index for the Tokyo Stock Exchange. The
Nikkei 225 index for the period 1990-2010 can be modeled by
V (t) = 23,500e-0.0381t
where t is the number of years after 1990. Determine how many years after 1990 the
Nikkei 225 index reached $20,000.
Suppose customers arrive to a single server at the rate of 1/2 customers per minute. The capacity
of the server is 1/3 customers per minute. Both service time and interarrival times are assumed
to be exponential. Suppose the system is initially empty. As the system unfolds, its inventory (in
process and waiting) will:
(a) reach a long-run average of 3 customers
(b) reach a long-run average of 2 customers
(c) stay in the system an average of 6 minutes
(d) grows unboundedly in the long-run
(e) None of the above
Chapter 9 Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Prob. 2ECh. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 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 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Explain why the functions with the given graphs...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Psychologists interested in learning theory study...Ch. 9.1 - Von Bertalanffys equation states that the rate of...Ch. 9.1 - Prob. 17ECh. 9.2 - A direction field for the differential equation y...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 19ECh. 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 - Prob. 27ECh. 9.3 - Solve the differential equation. 1. dydx=3x2y2Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Solve the differential equation. 5. (ey 1)y = 2 +...Ch. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 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 - Prob. 20ECh. 9.3 - Solve the differential equation y = x + y by...Ch. 9.3 - Solve the differential equation xy = y + xey/x by...Ch. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - An integral equation is an equation that contains...Ch. 9.3 - Prob. 35ECh. 9.3 - Find a function f such that f(3) = 2 and...Ch. 9.3 - Solve the initial-value problem in Exercise 9.2.27...Ch. 9.3 - Prob. 38ECh. 9.3 - In Exercise 9.1.15 we formulated a model for...Ch. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - A sphere with radius 1 m has temperature 15C. It...Ch. 9.3 - A glucose solution is administered intravenously...Ch. 9.3 - A certain small country has 10 billion in paper...Ch. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 54ECh. 9.4 - Prob. 1ECh. 9.4 - A population grows according to the given logistic...Ch. 9.4 - Prob. 3ECh. 9.4 - The Pacific halibut fishery has been modeled by...Ch. 9.4 - Suppose a population P(t) satisfies...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Biologists stocked a lake with 400 fish and...Ch. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Let c be a positive number. A differential...Ch. 9.4 - There is considerable evidence to support the...Ch. 9.4 - Another model for a growth function for a limited...Ch. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Solve the differential equation. 13....Ch. 9.5 - Solve the differential equation. 14....Ch. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Use the method of Exercise 23 to solve the...Ch. 9.5 - Prob. 26ECh. 9.5 - In the circuit shown in Figure 4, a battery...Ch. 9.5 - In the circuit shown in Figure 4, a generator...Ch. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Let P(t) be the performance level of someone...Ch. 9.5 - Prob. 32ECh. 9.5 - In Section 9.3 we looked at mixing problems in...Ch. 9.5 - A tank with a capacity of 400 L is full of a...Ch. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.6 - Prob. 1ECh. 9.6 - Each system of differential equations is a model...Ch. 9.6 - Prob. 3ECh. 9.6 - Lynx eat snowshoe hares and snowshoe hares eat...Ch. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 10ECh. 9.6 - In Example 1 we used Lotka-Volterra equations to...Ch. 9 - Prob. 1RCCCh. 9 - What can you say about the solutions of the...Ch. 9 - Prob. 3RCCCh. 9 - Prob. 4RCCCh. 9 - Prob. 5RCCCh. 9 - Prob. 6RCCCh. 9 - Prob. 7RCCCh. 9 - Prob. 8RCCCh. 9 - Prob. 9RCCCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 2RQCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 7RQCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Solve the differential equation. 5. y = xesin x y...Ch. 9 - Prob. 6RECh. 9 - Solve the differential equation. 7. 2yey2y=2x+3xCh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - A tank contains 100 L of pure water. Brine that...Ch. 9 - One model for the spread of an epidemic is that...Ch. 9 - The Brentano-Stevens Law in psychology models the...Ch. 9 - The transport of a substance across a capillary...Ch. 9 - Populations of birds and insects are modeled by...Ch. 9 - Prob. 23RECh. 9 - Barbara weighs 60 kg and is on a diet of 1600...Ch. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Find all functions f that satisfy the equation...Ch. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - Snow began to fall during the morning of February...Ch. 9 - Prob. 9PCh. 9 - Prob. 10PCh. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- In a printing shop, print requests arrive randomly and independently at anaverage rate of 20 per hour and are placed in a queue according to arrival times.Suppose that the time it takes to process each request is exponentiallydistributed and that the print times for different jobs are independent.A particular printer in this shop is capable of printing five pages perminute. The average request results in ten printed pages of poster. (i)There are currently five jobs in the queue – one active and fourwaiting to be processed. A new customer submit a job to this printerand it becomes the sixth job in the queue. Calculate the probabilitythat he will have to wait more than 5 minutes for the printer tobegin processing his job. Assume that the time between consecutivejobs in the queue is negligible.(ii) Name the alternative distribution of the random variable that youare considering in (i)arrow_forward(2) The annual net profit for a company, from 1995 to 2005, can be approximated by the model an 10e0.2n, n = 1, 2, 3, ., N, where an is the annual net profit in millions of dollars, and n represents the year, with n =1 corresponding to 1995. Estimate the total net profit during this period. (3) A deposit of 15 dollars is made at the beginning of each month, for a period of 5 years, in an account that pays 0.9 % interest, compounded monthly. Find the balance in the account at the end of the 5 years. (4) A deposit of 20 dollars is made every 3 months, for a period of 10 years, in an account that pays 1% interest, compounded quarterly. Find the balance in the account at the end of the 10 years. (5) A deposit of $500 can be made with two options: earn 2% interest, compounded quarterly for 3 years, or earn 1.5%, compounded monthly for 3 years. Find the balance after 3 years of both options.arrow_forward1. If Adam invests $10000 in a retirement account with a 7% interest rate compounded annually, how long will it take until Adam's account has a balance of $8000? (The amount of money after x years is given by A = P(1+r)*. )arrow_forward
- A 8-year projection of population trends suggests that t years from now, the population of a certain community will be P(t) = t³ + 15t² + 21t+ 60 thousand people. (a) At what time during the 8-year period will the population be growing most rapidly? 6 (b) At what time during the 8-year period will the population be growing least rapidly? (c) At what time during the 8-year period will the rate of population growth be growing most rapidly?arrow_forward(4) Consider the constant rate of decrease of a certain microorganism. At the start, there are 12,000 microorganisms in a certain place. After 30 seconds, the population decreased to 8000. If the number of microorganisms is directly proportional to the constant rate of decay and such decrease in number continues at the same rate, then how many microorganisms will there be after 45 seconds?arrow_forward(ii) A state predicts that it will need $2.15 billion for construction of new roads and maintenance of existing roads in year 2025. It is forecast that 1.5 percent of the vehicle-fleet in that year will be electric vehicles with the remaining being gas powered vehicles. The population of the state is forecast to be 10 million persons in 2025 with the average number of vehicles owned per person being 0.75. It is projected that on average each vehicle will be driven 12,000 miles per year, with gas powered vehicles achieving an average gas consumption of 25 miles per gallon (mpg). If the state plans to raise 99 percent of the required revenue from gas powered vehicles and the remainder from electric vehicles, (a) Determine how much each gallon of gas sold should be taxed to achieve the revenue target (b) Determine what the annual flat tax for each electric vehicle should be to raise the appropriate revenue target; (c) If the state decides to raise the required revenue based on a tax per…arrow_forward
- 4arrow_forward3. a) Solve the following two equations. In(x – 2) – In(x + 3) = 1 i) ii) 4x-2 = 3x+3 b) An amount of OMR 1500 is deposited in a bank at an annual rate of 4% interest compounded continuously; find the number of years after which the amount will become OMR 1700.arrow_forward4. In the year 1950, the world population was 2.56 billion people. In 1960, the population grew to 3.04 billion. (a) Assuming that the population obeys the law of uninhibited constant growth, find a formula for the population for any time t. (b) According to your model, what should the population be in the year 2020. Compare with the current population. (c) What population does your model predict in the year 2030?arrow_forward
- Assume that the population of a city satisfies the logistic hypothesis: "The rate of change of population at any time is proportional to the product of the population at that time and the difference between capacity and population." We have the following data: capacity is 11,825,000, population in 1960 was 3,750,500, and population in 2000 was 4,215,500. (a) Set up and solve an Initial Value Problem to express the population of the city as a function of time. (b) Draw a graph of the population. (c) Calculate an estimate of the population in the year 2030.arrow_forwardhe annual revenue of Amazon.com rose from approximately $10.7 billion in 2006 to $34.2 billion in 2010.† (a) Use this information to find both a linear model and an exponential model for Amazon.com's annual revenue I (in billions of dollars) as a function of time t in years since 2000. (Round all coefficients to three significant digits.) linear model I(t) = exponential model I(t) = Which of these models would you judge to be more appropriate to the data shown below? t (Year since 2000) 6 7 8 9 10 I ($ billions) 10.7 14.8 19.2 24.5 34.2 The is more appropriate. (b) Use the better of the two models from part (a) to predict the 2008 figure and compare it with the actual figure above. (Round your answer to one decimal place.) The model yields an estimate of $ billion, which is not too far from the actual figure.arrow_forwardSome populations initially grow exponentially but eventually level off. Equations of the formP (t) = M/(1 + Ae-kt)where M, A, and k are positive constants, are called logistic equations andare often used to model such populations. Here M is called the carryingcapacity and represents the maximum population size that can be supported,and A =(M−P0 )/Powhere P0 is the initial population.(a) Compute lim t→∞P (t). Explain why your answer is to be expected. (b) Compute limM→∞P (t). (Note that A is defined in terms of M.) What kindof function is your result?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY