Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.5 - Linear Functions and Models - 2.5 Exercises - Page 197: 46

Answer

(a) $d(t) = 0.8t$ (b) Image below. (c) 48 mi/h

Work Step by Step

(a) Linear function: $d(t) = at + b$ Since she starts in Detroit, and we start counting the time there. (t =0 and d(t) = 0). $b=0$ $d(t) = at$ Substituting the values: $$40 = a(50) \longrightarrow a = \frac{40}{50} = 0.8$$ $$d(t) = 0.8t$$ (b) We already have 2 points (0,0) and (50,40). Plot these points, and draw the line that passes through both. (c) speed = slope = a = 0.8 But 0.8 represents the speed in (mi/min). Since $1 \space h = 60 \space min$ $$0.8 \frac{mi}{min} \times \frac{60 \space min}{1 \space h} = 48 \space mi/h$$
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