Skip to main content

Math Calculus Calculus & Its Applications

Car Prices in 2012 The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $ 30 , 303 in 2012 . A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay $ 500 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 3 ⋅ 5 % . (Source: The National Automobile Dealers Association, www.nada.com.) a. Set up a differential equation that is satisfied by the amount f ( t ) of money owed on the car loan at time t . b. How long will it take to pay off the car loan?

Car Prices in 2012 The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $ 30 , 303 in 2012 . A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay $ 500 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 3 ⋅ 5 % . (Source: The National Automobile Dealers Association, www.nada.com.) a. Set up a differential equation that is satisfied by the amount f ( t ) of money owed on the car loan at time t . b. How long will it take to pay off the car loan?

Solution Summary: The author explains how a differential equation is satisfied by the amount of money owed on the car loan at time t.

Calculus & Its Applications

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)

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Textbook Question

Chapter 10.4, Problem 8E

Car Prices in 2012 The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $ 30 , 303 in 2012 . A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay $ 500 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 3 ⋅ 5 % . (Source: The National Automobile Dealers Association, www.nada.com.)

a. Set up a differential equation that is satisfied by the amount f ( t ) of money owed on the car loan at time t .

b. How long will it take to pay off the car loan?

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 10.4, Problem 7E

Chapter 10.4, Problem 9E

Students have asked these similar questions

I circled the correct, could you explain using stoke

Use Euler's method to numerically integrate dy dx -2x+12x² - 20x +8.5 from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1

Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).

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. 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 - Prob. 2CYU 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. 2FCCE Ch. 10 - Prob. 3FCCE Ch. 10 - Prob. 4FCCE Ch. 10 - Prob. 5FCCE Ch. 10 - Prob. 6FCCE Ch. 10 - Prob. 7FCCE Ch. 10 - Prob. 8FCCE Ch. 10 - Prob. 9FCCE Ch. 10 - Prob. 10FCCE Ch. 10 - Prob. 11FCCE Ch. 10 - Prob. 12FCCE 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

Knowledge Booster

Background pattern image

$Calculus$

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

SEE MORE QUESTIONS

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning

Text book image

Glencoe Algebra 1, Student Edition, 9780079039897...

Algebra

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

Text book image

College Algebra

Algebra

ISBN:9781337282291

Author:Ron Larson

Publisher:Cengage Learning

Text book image

College Algebra

Algebra

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:Cengage Learning

Text book image

Intermediate Algebra

Algebra

ISBN:9780998625720

Author:Lynn Marecek

Publisher:OpenStax College

Text book image

College Algebra

Algebra

ISBN:9781938168383

Author:Jay Abramson

Publisher:OpenStax

Text book image

Intermediate Algebra

Algebra

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

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