Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In March $2011$ , Nicor Gas had the following rate schedule for natural gas usage in single-family residences:
Monthly customer charge $- $ 13.55$
Distribution charge
First $20$ therms $- 0.1473 / t h e r m$
Next $30$ therm $- $ 0.0579 / t h e r m$
Over $50$ therm $- $ 0.0519 / t h e r m$
Gas supply charge $- $ 0.51 / t h e r m$
(a) What is the charge for using $40$ therms in a month?
(b) What is the charge for using $150$ therms in a month?
(c) Develop a model that gives the monthly charge $C$ for $x$ therms of gas.
(d) Graph the function found in part (c).

(a) The charge for using $40$ therms in a month is $$ 38.054$

(b) The charge for using $150$ therms in a month is $$ 99.923$

(c) The model that gives the monthly charge $C$ for $x$ therms of gas is $C (x) = \{\begin{cases} 0.5619 x + 2.088, x > 50 \\ 0.5679 x + 1.788, x \leq 50 \end{cases}$

(d) The graph of the function found in part (c) is:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1. Given

Monthly customer charge $- $ 13.55$

First $20$ therms $- $ 0.1473 / t h e r m$

Next $30$ therms $- $ 0.0579 / t h e r m$

Over $50$ therms $- $ 0.0519 / t h e r m$

Gas supply charge $- $ 0.51 / t h e r m$

Part (a) Step 2. Find the distribution charge and gas charge

The distribution charge for first $20$ therms is

$= 0.1473 \times 20 = $ 2.946$

The distribution charge for the next $20$ therms is

$= 0.0579 \times 20 = $ 1.158$

Gas charge for $40$ therms $= 0.51 \times 40$

$= $ 20.4$

Part (a) Step 3. Add the terms found above.

Charge for using $40$ therms in a month $= 13.55 + 2.946 + 1.158 + 20.4 = $ 38.054$

Part (b) Step 1. Find the distribution charge and gas charge

Referring to part (a), the distribution charge for using first $20$ therms is $$ 2.946$

The distribution charge for the next $30$ therms $= 0.0579 \times 30$

$= $ 1.737$

The distribution charge for next $100$ therms,

$= 0.0519 \times 100 = $ 51.9$

Gas charge for $150$ therms $= 0.51 \times 150$

$= $ 76.5$

Part (b) Step 2. Find the total charge

Monthly service charge $= $ 13.55$

Total charge for using $150$ therms is given by,

$= 13.55 + 2.946 + 1.737 + 5.19 + 76.5 = $ 99.923$

Part (c) Step 1. To find the charges for therms

Monthly charge $= $ 13.55$

Referring to part (a), (b), the distribution charge for $20$ therms is $$ 2.946$ and the distribution charge for next $30$ therm is $$ 1.737$

The distribution charge for next $(x - 50)$ therms is,

$= 0.0519 (x - 50) = 0.0519 x - 2.595$

The gas charge for $x$ therms $= 0.51 x$

Part (c) Step 2. Find model C for x therms for x≥50

For $x \geq 50$ the total charge is given by

$C (x) = 2.946 + 1.737 + 0.0519 x - 2.595 + 0.51 x = 0.5619 x + 2.088$

Part (c) Step 3. Find the model for x<50

The total charge for $x$ terms if $x < 50$ is given by,

$= 0.0579 (x - 20) = 0.0579 x - 1.158$

Total charge for $x$ therms $C (x) = 2.946 + 0.0579 x - 1.158 + 0.51 x = 0.5679 x + 1.788$

Part (d) Step 1. Graph the function in part (c)

Graph the function $C (x) = \{\begin{cases} 0.5619 x + 2.088, x > 50 \\ 0.5679 x + 1.788, x \leq 50 \end{cases}$

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Short Answer

Step by Step Solution

Part (a) Step 1. Given

Part (a) Step 2. Find the distribution charge and gas charge

Part (a) Step 3. Add the terms found above.

Part (b) Step 1. Find the distribution charge and gas charge

Part (b) Step 2. Find the total charge

Part (c) Step 1. To find the charges for therms

Part (c) Step 2. Find model C for x therms for x≥50

Part (c) Step 3. Find the model for x<50

Part (d) Step 1. Graph the function in part (c)

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Precalculus Enhanced with Graphing Utilities

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Short Answer

Step by Step Solution

Part (a) Step 1. Given

Part (a) Step 2. Find the distribution charge and gas charge

Part (a) Step 3. Add the terms found above.

Part (b) Step 1. Find the distribution charge and gas charge

Part (b) Step 2. Find the total charge

Part (c) Step 1. To find the charges for therms

Part (c) Step 2. Find model C for x therms for x≥50

Part (c) Step 3. Find the model for x<50

Part (d) Step 1. Graph the function in part (c)

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