Calculus & Its Applications
15th Edition
ISBN: 9780137590896
Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti
Publisher: Pearson Education (US)
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5.4, Problem 1E
To determine
To find: The initial value problem for the problem.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
2)
An initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years?
R) - 10,000(1.11)
R) - 10,000(1.11)
- 10,000(11)'
A) – 10,000(0.11)'
a.
c.
b.
d.
(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.
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.
Chapter 5 Solutions
Calculus & Its Applications
Ch. 5.1 - a. Solve the differential equation...Ch. 5.1 - Under ideal conditions a colony of Escherichia...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...
Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - Population and Exponential Growth Let P(t) be the...Ch. 5.1 - Growth of a Colony of Fruit Flies A colony of...Ch. 5.1 - GrowthConstant for a Bacteria Culture Abacteria...Ch. 5.1 - Growth of a Bacteria Culture The initial size of a...Ch. 5.1 - Using the Differential Equation Let P(t) be the...Ch. 5.1 - Growth of Bacteria Approximately 10,000 bacteria...Ch. 5.1 - Growth of cells After t hours, there are P(t)...Ch. 5.1 - Insect Population The size of a certain insect...Ch. 5.1 - Population Growth Determine the growth constant of...Ch. 5.1 - Time to Triple Determine the growth constant of a...Ch. 5.1 - Exponential Growth A population is growing...Ch. 5.1 - Time to DoubleA population is growing...Ch. 5.1 - Exponential Growth The rate of growth of a certain...Ch. 5.1 - Worlds Population The worlds population was 5.51...Ch. 5.1 - Prob. 33ECh. 5.1 - A Population Model The population (in millions) of...Ch. 5.1 - Radioactive Decay A sample of 8 grams of...Ch. 5.1 - Radioactive Decay Radium 226 is used in cancer...Ch. 5.1 - Decay of Penicillin in the Bloodstream A person is...Ch. 5.1 - Radioactive Decay Ten grams of a radioactive...Ch. 5.1 - Radioactive Decay The decay constant for the...Ch. 5.1 - Drug ConstantRadioactive cobalt 60 has a half-life...Ch. 5.1 - Iodine Level in Dairy Products If dairy cows eat...Ch. 5.1 - Half-Life Ten grams of a radioactive material...Ch. 5.1 - Decay of Sulfate in the Bloodstream In an animal...Ch. 5.1 - Radioactive Decay Forty grams of a certain...Ch. 5.1 - Radioactive Decay A sample of radioactive material...Ch. 5.1 - Rate of Decay A sample of radioactive material has...Ch. 5.1 - Carbon Dating In 1947, a cave with beautiful...Ch. 5.1 - King Arthur's Round Table According to legend, in...Ch. 5.1 - Prob. 49ECh. 5.1 - Population of the PacificNorthwest In 1938,...Ch. 5.1 - Time of the Fourth Ice Age Many scientists believe...Ch. 5.1 - Time Constant Let T be the time constant of the...Ch. 5.1 - Prob. 53ECh. 5.1 - Time Constant and Half-life Consider as...Ch. 5.1 - An Initial Value Problem Suppose that the function...Ch. 5.1 - Time to Finish Consider the exponential decay...Ch. 5.2 - One thousand dollars is to be invested in a bank...Ch. 5.2 - A building was bought for 150,000 and sold 10...Ch. 5.2 - Savings Account Let A(t)=5000e0.04t be the balance...Ch. 5.2 - Savings Account Let A(t) be the balance in a...Ch. 5.2 - Savings Account Four thousand dollars is deposited...Ch. 5.2 - Savings Account Ten thousand dollars is deposited...Ch. 5.2 - Investment AnalysisAn investment earns 4.2 yearly...Ch. 5.2 - Investment Analysis An investment earns 5.1 yearly...Ch. 5.2 - Continuous Compound One thousand dollars is...Ch. 5.2 - Continuous Compound Ten thousand dollars is...Ch. 5.2 - Technology Stock One hundred shares of a...Ch. 5.2 - Appreciation of Art Work Pablo Picassos Angel...Ch. 5.2 - Investment Analysis How many years are required...Ch. 5.2 - Doubling an Investment What yearly interest rate...Ch. 5.2 - Tripling an Investment If an investment triples in...Ch. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Real Estate Investment A farm purchased in 2000...Ch. 5.2 - Real Estate Investment A parcel of land bought in...Ch. 5.2 - Present Value Find the present value of 1000...Ch. 5.2 - Prob. 20ECh. 5.2 - Present Value How much money must you invest now...Ch. 5.2 - Present Value If the present value of 1000 to be...Ch. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Differential Equation and InterestA small amount...Ch. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 2ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 6ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 8ECh. 5.3 - Percentage Rate of Growth The annual sales S(in...Ch. 5.3 - Prob. 10ECh. 5.3 - Price of Ground Beef The wholesale price in...Ch. 5.3 - Price of Pork The wholesale price in dollars of...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 14ECh. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 18ECh. 5.3 - Elasticity of Demand Currently 1800 people ride a...Ch. 5.3 - Prob. 20ECh. 5.3 - Elasticity of Demand A movie theater has a seating...Ch. 5.3 - Prob. 22ECh. 5.3 - Elasticity of Demand A country that is the major...Ch. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.4 - A sociological study was made to examine the...Ch. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5 - What differential equation is key to solving...Ch. 5 - Prob. 2FCCECh. 5 - Prob. 3FCCECh. 5 - Explain how radiocarbon dating works.Ch. 5 - Prob. 5FCCECh. 5 - Prob. 6FCCECh. 5 - Define the elasticity of demand, E(p), for a...Ch. 5 - Describe an application of the differential...Ch. 5 - Prob. 9FCCECh. 5 - Atmospheric Pressure The atmospheric pressure...Ch. 5 - Population Model The herring gull population in...Ch. 5 - Present Value Find the present value of 10,000...Ch. 5 - Compound Interest One thousand dollars is...Ch. 5 - Half-Life The half-life of the radioactive element...Ch. 5 - Carbon Dating A piece of charcoal found at...Ch. 5 - Population Model From January 1, 2010, to January...Ch. 5 - Compound Interest A stock portfolio increased in...Ch. 5 - Comparing Investments An investor initially...Ch. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RE
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
- Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.arrow_forwardAnnual U.S. imports from a certain country in the years 1996 through 2003 can be approximated by I(t) + 3.6 +47 (1st s9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to this country in the same years can be approximated by E(t) 0.5²-1.4t+16 (0 sts 10) billion dollars. Assuming the trends shown in the above models continue indefinitely, numerically estimate the following. (If an answer does not exist, enter DNE.) im E(t) and lim 7-*** lim e(t)- E(t) lim 1-+= 1(1) - E(E) (1)arrow_forward4- The gross domestic product (GDP) of a certain country was N(t) = t² + 5t + 106 billion dollars t years after 2018. a. At what rate was the GDP changing with respect to time in 2028? b. At what percentage rate was the GDP changing with respect to time in 2028?arrow_forward
- Chapter 1, Section 1.5, Question 002 Each of the following functions gives the amount of a substance present at time t. In each case, give the amount present initially (at t = 0), state whether the function represents exponential growth or decay, and give the percent rate. Enter the exact answers. (a) A = 70(1.08)' The initial amount is | and it represents | with rate %. (b) A = 4.08(0.969)' The initial amount is and it represents with rate %. (c) A = 4500(1.03)arrow_forwardThe table shows the total assets (in trillions) held in a foreign bank for the given years. Complete parts (a) through (c) below. Year Assets 2000 | 2005 | 2007 | 2009 | 2011 | 2013 | 2015 16 40 54 80 117 152 200 (a) Find an exponential model of the form f(t) = yob' for these data, where t= 0 corresponds to the year 2000. If you do not have suitable technology, use the first and pre last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function. The exponential model for the data is f(t) = D. (Round to three decimal places as needed.) tion 1 sti stion 5arrow_forwardhe table shows the total assets (in trillions) held in a foreign bank for the given years. Complete parts (a) through (c) below. Year 2000 | 2005 | 2007 | 2009 | 2011 | 2013 | 2015 Assets 16 40 54 80 117 152 200 (a) Find an exponential model of the form f(t) =yob' for these data, where t= 0 corresponds to the year 2000. If you do not have suitable technology, use the first and last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function. The exponential model for the data is f(t) =WD. (Round to three decimal places as needed.)arrow_forward
- Present value is the amount of money that must be invested now at a given rate of interest to produce a given future value. For a 1-year investment, the present value can be calculated using Present value = Future value 1 + r , where r is the yearly interest rate expressed as a decimal. (Thus, if the yearly interest rate is 8%, then 1 + r = 1.08.) If an investment yielding a yearly interest rate of 13% is available, what is the present value of an investment that will be worth $4000 at the end of 1 year? That is, how much must be invested today at 13% in order for the investment to have a value of $4000 at the end of a year? (Round your answer to two decimal places.)arrow_forwardAt the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation. The global cruising industry has been growing at approximately 7% per year. Assume that this growth rate continues. Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t. Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part. (a) Report the following. Use the pull-down menu to indicate the units. A0) = Number Click for List (b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1? O b is greater than 1 O b is less than 1 (c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years. Do not round any values. Since your formula gives N in millions of people, check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000. N= Number ( Number (d) How many millions of cruise…arrow_forward2. Many countries have a population growth rate of 3% (or more) per year. At this rate, how many years will it take a population to double? Use the model A = Aoert.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
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