Concept explainers
Isocost Equation We are to buy quantities of two items:
a. If item 1 costs $3.50 per unit and item 2 costs $2.80 per unit, find a formula that gives the total cost
b. An isocost equation shows the relationship between the number of units of each of two items to be purchased when the total purchase price is predetermined. If the total purchase price is predetermined to be
c. Solve for
d. Using the equation from part c, determine how many units of item 1 are to be purchased if 18 units of item 2 are purchased.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Intermediate Algebra for College Students (7th Edition)
College Algebra (6th Edition)
Glencoe Algebra 2 Student Edition C2014
Algebra and Trigonometry (6th Edition)
College Algebra: Graphs and Models (6th Edition)
Elementary Algebra: Concepts and Applications (10th Edition)
- Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forwardDistance and time Anthony leaves Kingstown at 2:00 PM and drives to Queenville, 160 mi distant, at 45mi/h .At 2:15 PM. Helen leaves Queensville and drives to Kingstown at 40 mi/h . At what time do they pass each other on the road?arrow_forwardMeasurement Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters y to gallons x. Then use the model to find the numbers of liters in 5 gallons and 25 gallons.arrow_forward
- Gas Mileage The distance d, in miles, that you can travel without stopping for gas depends on the number of gallons g of gasoline in your tank and the gas mileage m, in miles per gallon, that your car gets. The relationship is d=gm. 2.5 a. How far can you drive if you have 12 gallons of gas in your tank and your car gets 24 miles per gallon? b. Solve Equation 2.5 for m. i. Explain in everyday terms what this new equation means. ii. Use this equation to determine the gas mileage of your car if you can drive 335 miles on a full 13-gallon tank of gas. c. A Detroit engineer wants to be sure that the car she is designing can go 425 miles on a full tank of gas, and she must design a gas tank to ensure that. She does not yet know what gas mileage this new-model car will get, and so she decides to make a graph of the size of the gas tank as a function of gas mileage. i. Solve Equation 2.5 for g using 425 for the distance. ii. Make the graph that the engineer made. Is it a straight line?arrow_forwardProfit = revenue cost Cost and Revenue A tire company determines that to manufacture a certain type of tire, it costs $8000 to set up the production process. Each tire that is produced costs $22 in material and labor. The company sells this tire to wholesale distributors for $49 each. (a) Find a formula for the cost C of producing x tires? (b) Find a formula for the revenue R from selling x ? (c) Find a formula for the profit P from selling x tires? (d)How many tires must the company sell to break even?arrow_forwardDistance and Time Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 mi distant, at 45 mi/h. at 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/h. At what time do they pass each other on the road?arrow_forward
- Measurement Use the fact that 13 inches is approximately the same length as 33 centimeters to find a mathematical model that relates centimeters y to inches x. Then use the model to find the numbers of centimeters in 10 inches and 20 inches.arrow_forwardAlexanders Formula One interesting problem in the study of dinosaurs is to determine from their tracks how fast they ran. The scientist R. McNeil Alexander developed a formula giving the velocity of any running animal in terms of its stride length and the height of its hip above the ground. The stride length of dinosaur can be measured from successive prints of the same foot, and the hip height roughly the leg length can be estimated on the basis of the size of a footprint, so Alexanders formula gives a way of estimating from dinosaur tracks how fast the dinosaur was running. See Figure 2.45. If the velocity v is measured in meters per second, and the stride length s and hip height h are measured in meters, then Alexanders formula is v=0.78s1.67h1.17. For comparison, a length of 1 meter is 39.37inches, and a velocity of 1 meter per second is about 2.2milesperhour. First, we study animals with varying stride lengths, but all with a hip height of 2meters so h=2 i. Find the formula for the velocity v as a function of the stride length s. ii. Make a graph of v versus s. Include stride lengths from 2to10meters. iii. What happens to the velocity as the stride length increases? Explain your answer in practical terms. iv. Some dinosaur tracks show a stride length of 3meters, and a scientist estimates that the hip height of the dinosaur was 2meters. How fast was the dinosaur running?arrow_forwardMeasurement A billboard says that it is 12.5 miles or 20 kilometers to the next gas station. Use this information to find a mathematical model that relates miles x to kilometers y. Then use the model to find the numbers of kilometers in 5 miles and 25 miles.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill