Calculus & Its Applications
Calculus & Its Applications
12th Edition
ISBN: 9780137590810
Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti
Publisher: PEARSON
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
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Chapter 10.7, Problem 11E

Suppose that the consumer Products Safety Commission issues new regulations that affect the toy manufacturing industry. Every toy manufacturer will have to make certain changes in it’s manufacturing process. Let f ( t ) be the fraction of manufacturers that have complied within t months. Note that 0 ≤ f ( t ) ≤ 1 . Suppose that the rate at which new companies comply with the regulations is proportional to the fraction of companies, who have not yet complied, with constant of proportionality k = 0.1 .

Construct a differential equation satisfied by f ( t ) .

Use Euler’s method with n = 3 to estimate the fraction of companies that comply with the regulations within the first 3 months.

Solve the differential equation in part (a) and compute f ( 3 ) .

Compare the answers in part (b) and (c) and approximate the error in using Euler’s method.

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Chapter 10 Solutions

Calculus & Its Applications

Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYUCh. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Is the constant function f(t)=3 a solution of the...
Ch. 10.1 - Prob. 8ECh. 10.1 - Find a constant solution of y=t2y5t2.Ch. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Savings Account Let f(t) be the balance in a...Ch. 10.1 - Spread of News A certain piece of news is being...Ch. 10.1 - Paramecium Growth Let f(t) be the size of...Ch. 10.1 - Rate of Net Investment Let f(t) denote the amount...Ch. 10.1 - Newtons Law of Cooling A cool object is placed in...Ch. 10.1 - Carbon Dioxide Diffusion in Lungs during Breath...Ch. 10.1 - Slope Field The slope field in Fig4(a) suggests...Ch. 10.1 - Prob. 23ECh. 10.1 - On the slope field in Fig5(a), or a copy of it,...Ch. 10.1 - Prob. 25ECh. 10.1 - On the slope field in Fig4(a), or a copy of it,...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Technology Exercise Consider the differential...Ch. 10.1 - Technology Exercise The function f(t)=50001+49et...Ch. 10.2 - Solve the initial-value problem y=5y,y(0)=2, by...Ch. 10.2 - Solve y=ty,y(1)=4.Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 23ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Probability of AccidentsLet t represent the total...Ch. 10.2 - Amount of Information LearnedIn certain learning...Ch. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Rate of DecompositionWhen a certain liquid...Ch. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.3 - Using an integrating factor, solve y+y=1+et.Ch. 10.3 - Find an integrating factor for the differential...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the initial value problem: y+2y=1,y(0)=1.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem: y=2(10y),y(0)=1.Ch. 10.3 - Solve the initial value problem: y+y=e2t,y(0)=1.Ch. 10.3 - Solve the initial value problem: tyy=1,y(1)=1,t0.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Consider the initial value problem...Ch. 10.4 - Solutions can be found following the section...Ch. 10.4 - A Retirement Account refer toExample 1 a. How fast...Ch. 10.4 - Prob. 2ECh. 10.4 - A Retirement Account A person planning for her...Ch. 10.4 - A Savings Account A person deposits 10,000 in bank...Ch. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Aperson took out a loan of 100,000 from a bank...Ch. 10.4 - Car Prices in 2012 The National Automobile Dealers...Ch. 10.4 - New Home Prices in 2012 The Federal Housing...Ch. 10.4 - Answer parts (a), (b), and (c) of Exercise 9 if...Ch. 10.4 - Prob. 11ECh. 10.4 - Find the demand function if the elasticity of...Ch. 10.4 - Temperature of a Steel Rod When a red-hot steel...Ch. 10.4 - Prob. 14ECh. 10.4 - Determining the Time of Death A body was found in...Ch. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Radioactive Decay Radium 226 is a radioactive...Ch. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 22ECh. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Technology Exercise Therapeutic Level of a Drug A...Ch. 10.5 - Consider the differential equation y=g(y) where...Ch. 10.5 - Prob. 2CYUCh. 10.5 - Prob. 3CYUCh. 10.5 - Prob. 4CYUCh. 10.5 - Exercise 1-6 review concepts that are important in...Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Ch. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Ch. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - , where , and Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Growth of a plant Suppose that, once a sunflower...Ch. 10.5 - Prob. 38ECh. 10.5 - Technology Exercises Draw the graph of, and use...Ch. 10.5 - Technology Exercises Draw the graph of...Ch. 10.6 - Refer to Example 4, involving the flow of...Ch. 10.6 - Prob. 2CYUCh. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 2ECh. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 4ECh. 10.6 - Answer part (a) in Example 2, if the pond was...Ch. 10.6 - Prob. 6ECh. 10.6 - Social Diffusion For information being spread by...Ch. 10.6 - Gravity At one point in his study of a falling...Ch. 10.6 - Autocatalytic Reaction In an autocatalytic...Ch. 10.6 - Drying A porous material dries outdoors at a rate...Ch. 10.6 - Movement of Solutes through a Cell Membrane Let c...Ch. 10.6 - Bacteria Growth An experimenter reports that a...Ch. 10.6 - Chemical Reaction Suppose that substance A is...Ch. 10.6 - War Fever L. F. Richardson proposed the following...Ch. 10.6 - Capital Investment Model In economic theory, the...Ch. 10.6 - 16. Evans Price Adjustment Model Consider a...Ch. 10.6 - Fish Population with Harvesting The fish...Ch. 10.6 - Continuous Annuity A continuous annuity is a...Ch. 10.6 - Savings Account with Deposits A company wishes to...Ch. 10.6 - Savings Account A company arranges to make...Ch. 10.6 - Amount of CO2 in a Room The air in a crowded room...Ch. 10.6 - Elimination of a Drug from the Bloodstream A...Ch. 10.6 - Elimination of a Drug A single dose of iodine is...Ch. 10.6 - Litter in a Forest Show that the mathematical...Ch. 10.6 - Population Model In the study of the effect of...Ch. 10.7 - Prob. 1CYUCh. 10.7 - Prob. 2CYUCh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Use Eulers method with n=4 to approximate the...Ch. 10.7 - Let be the solution of , Use Euler’s method with...Ch. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Suppose that the consumer Products Safety...Ch. 10.7 - 12. Rate of evaporation The Los Angeles plans to...Ch. 10.7 - Prob. 13ECh. 10.7 - The differential equation y=0.5(1y)(4y) has five...Ch. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10 - What is a differential equation?Ch. 10 - Prob. 2FCCECh. 10 - Prob. 3FCCECh. 10 - Prob. 4FCCECh. 10 - Prob. 5FCCECh. 10 - Prob. 6FCCECh. 10 - Prob. 7FCCECh. 10 - Prob. 8FCCECh. 10 - Prob. 9FCCECh. 10 - Prob. 10FCCECh. 10 - Prob. 11FCCECh. 10 - Prob. 12FCCECh. 10 - Describe Eulers method for approximating the...Ch. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Solve the differential equation in Exercises 1-10....Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Let P(t) denote the price in dollars of a certain...Ch. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Sketch the solutions of the differential equations...Ch. 10 - Sketch the solutions of the differential equations...Ch. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Suppose that in a chemical reaction, each gram of...Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Let f(t) be the solution to y=2e2ty,y(0)=0. Use...Ch. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RE
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