Concept explainers
Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number
17. How Much Can I Borrow? The function in Example 1.2 can be rearranged to show the amount of money
Suppose you can afford to pay $350 per month for 4 years.
a. How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is a 9% APR.) Express the answer in functional notation, and then calculate it.
b. Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or a 3% APR). How much can you afford to borrow now?
c. Even at a 3% APR, you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 5 years. How much can you afford to borrow under these conditions?
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. 13. Radioactive Substances change form over time. For example, carbon 14, which is important for radiocarbon dating, changes through radiation into nitrogen. If we start with 5 grams of carbon 14, then the amount C=C(t) of carbon 14 remaining after t years is given by C=50.5t/5730 a. Express the amount of carbon 14 left after 800 years in functional notation, and then calculate its value. b. How long will it take before half of the carbon 14 is gone? Explain how you got your answer. Hint: You might use trial and error to solve this, or you might solve it by looking carefully at the exponent..arrow_forwardRemainder: Round all answer to two decimal places unless otherwise indicated. a. How much does the stationery alone cost for a 3-page letter? b. How much does it cost to prepare and mail a 3-page letter if your secretary spends 2 hours on typing and corrections? c. Use a formula to express the cost of the stationery alone for a letter as a function of the number of pages in the letter. Identify the function and each of the variables you use, and state the units. d. Use a formula to express the cost of preparing and mailing a letter as a function of the number of pages in the letter and the time it takes your secretary to type it. Identify the function and each of the variables you use, and state the units. e. Use the function you made in part d to find the cost of preparing and mailing a 2-page letter that it takes your secretary 25 minutes to type.arrow_forwardWhat Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Time to Pay Off a Loan The function T(P,r,m) gives the time required to pay off an installment loan of P dollars if the APR is r as a decimal and we make monthly payments of in dollars. Use functional notation to indicate the time required to pay off a 12,000 automobile loan at an APR of 5 if the monthly payment is 450.arrow_forward
- Round all answers to two decimal places unless otherwise indicated. Investment Balance You invest B0 dollars in an account that draws interest at a monthly rate of r as a decimal, compounded monthly. After t months, the balance in dollars is given by B=B0(1+r)t. a. Let a denote the APR as a decimal. Then the monthly rate as a decimal is equal to a divided by 12. Express the balance in terms of initial investment, the number of months, and the APR as a decimal. b. Let a denote the APR as a decimal, and let A denote the APR as a percentage. Then a is equal to A divided by 100. Express the balance in terms of initial investment, the number of months, and the APR as a percentage. c. Note that y years is equivalent to 12y months. Express the balance in terms of the initial investment, the number y of years, and the APR as a percentage.arrow_forwardGrowth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Sleeping Longer A certain man observed that each night he was sleeping 15 minutes longer than he had the night before, and he used this observation to predict the day of his death. 9 If he made his observation right after sleeping 8 hours, how long would it be until he slept 24 and so would never again wake?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Composing Functions Use a formula to express y as a function of t if y=3x2+5x and x=t1.arrow_forwardGetting a Formula In Exercises S-4 through S-13, a verbal description of a function is given. Use a formula to express the function. With no advertising, your newspaper has a circulation of 8000 papers. For each dollar you spend on advertising, your newspaper circulation increased by 5 papers. You earn a profit taking into account advertising expense of 7 cents for each paper sold, but you must pay 400 to have the papers delivered. Find a formula that gives the total profit P, in dollars, that you earn if you spend a dollars on advertising.arrow_forwardradioactive Decay These exercises use the population radioactive Decay. Radioactive Cesium The half-life of cesium- 37 is 30 years. Suppose we have a sample. (a) Find a function m(t)=m0et/k that mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample Will remain after 80 years? (d) After how many years will only 2 g of the sample remain?arrow_forward
- Reminder Round all answers to decimal places unless otherwise indicated. Health Plan The managers of an employee health plan for a firm have studied the balance B, in millions of dollars, in the plan account as a function of t, the number of years since the plan was instituted. They have determined that the rate of change dBdt in the account balance is given by the formula dBdt=10e0.1t12. a. Use your calculator to make a graph of dBdt versus t over the first 5 years of the plan. b. During what period is the account balance B decreasing? c. At what time is the account balance B at its minimum?arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. A Leaking Can The side of a cylindrical can full of water springs a leak, and the water begins to stream out. See Figure 5.73. The depth H, in inches, of water remaining in the can is a function of the distance D in inches measured from the base of the can at which the stream of water strikes the ground. Here is a table of values of D and H: Distance D, in inches Depth H, in inches 0 1.00 1 1.25 2 2.00 3 3.25 4 5.00 a. Use regression to find a formula for H as a quadratic function of D. b. When the depth is 4 inches, how far from the base of the can will the water stream strike the ground? c. When the water stream strikes the ground 5 inches from the base of the can, what is the depth of water in the can?arrow_forwardGrowth in Weight and Height Between the ages of 7 and 11 years, the weight w, in pounds, of a certain girl is given by the formula w=8t. Here t represents her age in years. a. Use a formula to express the age t of the girl as a function of her weight w. b. At what age does she attain a weight of 68 pounds? c. The height h, in inches, of this girl during the same period is given by the formula h=1.8t+40. i. Use you answer to part b to determine how tall she is when she weighs 68 pounds. ii. Use a formula to express the height h of the girl as a function of her weight w. iii. Answer the question in part i again, this time using your answer to part ii.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage