Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 34: 20


(a) $C = 0.25d + 260$ (b) $\$635$ (c) Graph shown in image. The slope represents the price of fuel per mile per month. (d) The C-intercept represents some fixed monthly payment outside the costs of fuel (e.g. installments for paying for the car, price of scheduled maintenance every month, etc.) (e) The price of fuel per mile per month generally does not change significantly, thus the cost can suitably be modeled linearly (ie. with a constant slope).

Work Step by Step

(a) The slope can be found as follows: $m = \frac{460-380}{800-480} = 0.25$ The C-intercept is found by inputting the given x-values (miles) into the equation $C = 0.25d$ and adjusting for the difference. For example: $C = 0.25(800) = 200$ The actual C should be $460$. Thus, C is: $C = 460-200 = 260$ This is checked by doing the same for the other pair of values. The complete equation is thus: $C = 0.25d + 260$ (b) Using the equation found in (a): $C = 0.25(1500) + 260 = 635$ (c) Plot two points of the function and join them to find the graph. The meaning of the slope is found by considering that it adds to the monthly cost with greater distance travelled (ie. it is the monthly cost per unit distance travelled), which is likely the cost of fuel. (d) The meaning of the C-intercept is found by considering that even at 0 miles travelled, there is still a cost of $260 every month, meaning there is a fixed monthly payment of some kind. (e) Linear functions can give suitable models when the rate of change (ie. the slope) stays approximately constant. The price of fuel does not fluctuate much in most countries, so this fulfills that criteria (since we've established in (c) that the slope represents the cost of fuel per mile per month).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.