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: 50

Answer

(a) $C(x) = 13x + 900$ (b) Image below. Slope = 13 (c) $13 per chair

Work Step by Step

(a) If $C(x)$ represents the cost of producing x chairs: $$C(x) = ax + b$$ $$a = \frac{4800 - 2200}{300 - 100} = \frac{2600}{200} = 13$$ Now, substitute some of the values into the equation to find the $b$ value. $$C(x) = ax + b \longrightarrow 2200 = (13)(100) + b$$ $$2200 = 1300 + b$$ $$b = 2200 - 1300 = 900$$ $$C(x) = 13 x + 900$$ (b) Plot the following points: $(100,2200)$ and $(300,4800)$. Then draw the line that passes through both points. Slope = a = 13 (c) Rate of change (cost increase) = a = $13$ Since $C(x)$ is in $\$$ and $x$ in number of chairs: $\$13 \space per \space chair $
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