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Math Calculus Mymathlab With Pearson Etext -- Standalone Access Card -- For Calculus & Its Applications With Integrated Review Format: Access Card Package

Probability of AccidentsLet t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p ( t ) represent the probability that the driver will have at least one accident during these t hours. Then, 0 ≤ p ( t ) ≤ 1 , and 1 − p ( t ) represent the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of t ) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.

Probability of AccidentsLet t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p ( t ) represent the probability that the driver will have at least one accident during these t hours. Then, 0 ≤ p ( t ) ≤ 1 , and 1 − p ( t ) represent the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of t ) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.

Solution Summary: The author explains the construction and the solution of the differential equation that describes the situation about Probability of Accidents.

Mymathlab With Pearson Etext -- Standalone Access Card -- For Calculus & Its Applications With Integrated Review Format: Access Card Package

Mymathlab With Pearson Etext -- Standalone Access Card -- For Calculus & Its Applications With Integrated Review Format: Access Card Package

14th Edition

ISBN: 9780134776576

Author: Goldstein, Larry J^lay, David^asmar, Nakhle^schneider, David I

Publisher: Prentice Hall

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Textbook Question

Chapter 10.2, Problem 33E

Probability of AccidentsLet t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p ( t ) represent the probability that the driver will have at least one accident during these t hours. Then, 0 ≤ p ( t ) ≤ 1 , and 1 − p ( t ) represent the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of t ) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.

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Chapter 10.2, Problem 32E

Chapter 10.2, Problem 34E

Chapter 10 Solutions

Mymathlab With Pearson Etext -- Standalone Access Card -- For Calculus & Its Applications With Integrated Review Format: Access Card Package

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. 3CYU Ch. 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. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Is the constant function f(t)=3 a solution of the...

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. How fast...Ch. 10.4 - Prob. 2E Ch. 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. 5E Ch. 10.4 - Prob. 6E Ch. 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. 11E Ch. 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. 14E Ch. 10.4 - Determining the Time of Death A body was found in...Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Radioactive Decay Radium 226 is a radioactive...Ch. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 22E Ch. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 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. 2CYU Ch. 10.5 - Prob. 3CYU Ch. 10.5 - Prob. 4CYU Ch. 10.5 - Exercise 1-6 review concepts that are important in...Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E 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 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Ch. 10.5 - Prob. 27E Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10.5 - Prob. 33E Ch. 10.5 - , where , and Ch. 10.5 - Prob. 35E Ch. 10.5 - Prob. 36E Ch. 10.5 - Growth of a plant Suppose that, once a sunflower...Ch. 10.5 - Prob. 38E Ch. 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 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 2E Ch. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 4E Ch. 10.6 - Answer part (a) in Example 2, if the pond was...Ch. 10.6 - Prob. 6E Ch. 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. 1CYU Ch. 10.7 - Prob. 2CYU Ch. 10.7 - Prob. 1E Ch. 10.7 - Prob. 2E Ch. 10.7 - Prob. 3E Ch. 10.7 - Prob. 4E Ch. 10.7 - Prob. 5E Ch. 10.7 - Prob. 6E Ch. 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. 9E Ch. 10.7 - Prob. 10E Ch. 10.7 - Suppose that the consumer Products Safety...Ch. 10.7 - 12. Rate of evaporation The Los Angeles plans to...Ch. 10.7 - Prob. 13E Ch. 10.7 - The differential equation y=0.5(1y)(4y) has five...Ch. 10.7 - Prob. 15E Ch. 10.7 - Prob. 16E Ch. 10 - What is a differential equation?Ch. 10 - Prob. 2CCE Ch. 10 - Prob. 3CCE Ch. 10 - Prob. 4CCE Ch. 10 - Prob. 5CCE Ch. 10 - Prob. 6CCE Ch. 10 - Prob. 7CCE Ch. 10 - Prob. 8CCE Ch. 10 - Prob. 9CCE Ch. 10 - Prob. 10CCE Ch. 10 - Prob. 11CCE Ch. 10 - Prob. 12CCE Ch. 10 - Describe Eulers method for approximating the...Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Solve the differential equation in Exercises 1-10....Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Let P(t) denote the price in dollars of a certain...Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - Sketch the solutions of the differential equations...Ch. 10 - Sketch the solutions of the differential equations...Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - Suppose that in a chemical reaction, each gram of...Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Let f(t) be the solution to y=2e2ty,y(0)=0. Use...Ch. 10 - Prob. 30RE Ch. 10 - Prob. 31RE Ch. 10 - Prob. 32RE

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