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: 14

Answer

(a) See Graph Below (b) The slope represents the number of units of space omitted for every dollar increase. The y-int represents the maximum amount he can rent which is 200 spaces (the cost being 0). The x-int represents the amount he charges to rent 0 number of spaces.
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Work Step by Step

(a) Rough Graph of the linear function as shown. (b) The slope = x-coefficient = -4. If you let x=1, the number of units is 196. If you let x=2, the number of units is 192 - you subtract it by 4. Hence the slope represents the number of units of space that is unable to be rented for every dollar increased. The y-int occurs when x=0 - when the No. of units is 200. And this is the absolute maximum he can rent out if he made the cost 0. The x-intercept represents the amount he charges so that he is unable to rent any houses. This cost is $50.
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