Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises - Page 14: 61


a. $y=12,000x+3000$ b. $8.083$ years

Work Step by Step

a. The line (graph) contains points with coordinates (year, sales). Points on the graph (given by the text): (2, 27,000) , (5, 63,000). The slope is: $m=\displaystyle \frac{63,000-27,000}{5-2}=12,000$ Point-slope form of the line equation: $y-27,000=12,000(x-2)$ $y-27,000=12,000x-24, 000\qquad/+27,000$ $y=12,000x+3000$ b. Find x when $y=100,000$: Solve for x: $100, 000=12,000x+3000\qquad/-3000$ $97, 000=12, 000x\qquad /\div 12,000$ $8.083=x$ Sales would surpass \$ 100,000 after $8.083$ years.
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