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Math Calculus EBK CALCULUS & ITS APPLICATIONS

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.

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.

Solution Summary: The author explains that the differential equation satisfied by y=f(t) is the tion of manufacturers that have complied with the regulations within t months.

EBK CALCULUS & ITS APPLICATIONS

EBK CALCULUS & ITS APPLICATIONS

14th Edition

ISBN: 9780134507132

Author: Asmar

Publisher: YUZU

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Textbook Question

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 10.7, Problem 10E

Chapter 10.7, Problem 12E

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EBK CALCULUS & ITS APPLICATIONS

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Ch. 10.1 - Prob. 8E Ch. 10.1 - Find a constant solution of y=t2y5t2.Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 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. 23E Ch. 10.1 - On the slope field in Fig5(a), or a copy of it,...Ch. 10.1 - Prob. 25E Ch. 10.1 - On the slope field in Fig4(a), or a copy of it,...Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 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. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E 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 - Solve the following differential equations with...Ch. 10.2 - Prob. 23E Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Probability of AccidentsLet t represent the total...Ch. 10.2 - Amount of Information LearnedIn certain learning...Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - Prob. 37E Ch. 10.2 - Rate of DecompositionWhen a certain liquid...Ch. 10.2 - Prob. 39E Ch. 10.2 - Prob. 40E Ch. 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. 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