Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 198: 98

Answer

See below:
1568350845

Work Step by Step

Since the telephone billing plan is $\$60$ per month buys 450 minutes and the additional time costs $\$0.35$ per minute. So, the piecewise model function for telephone billing plan can be written as below: $C\left( t \right)=\left\{ \begin{align} & 60\text{ if 0}\le t\le 45\text{0} \\ & \text{60+0}\text{.35}\left( t-450 \right)\text{ if }t>450 \\ \end{align} \right.$ Solve the expression $\text{60+0}\text{.35}\left( t-450 \right)$ and write the expression in the simplified form as below: $\begin{align} & \text{60+0}\text{.35}\left( t-450 \right)=60+0.35t-0.35\times 450 \\ & =60+0.35t-157.5 \\ & =0.35t-97.5 \end{align}$ Thus, the simplified form of the expression for the telephone billing is as below: $C\left( t \right)=\left\{ \begin{align} & 60\text{ if 0}\le t\le 45\text{0} \\ & 0.35t-97.5\text{ if }t>450 \\ \end{align} \right.$ The function shown above consists of 2 straight lines. So the function can be written as $y=60$ for $0\le t\le 450$ and $y=0.35t-97.5$ for $t>450$
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