   Chapter 9.2, Problem 51E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Electrical usage costs The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function C ( x ) = { 20 + 0.188 x                if    0 ≤ x ≤ 100 38.80 + 0.15 ( x − 100 )  if    100< x ≤ 500 98.80 + 0.10 ( x − 500 )   if      x > 50 (a) What is the monthly charge if 1100 kWh of electricity is consumed in a month?(b) Find lim x → 100 C ( x ) a n d   lim x → 500 C ( x ) , if the limits exist.(c) Is C continuous at x = 100 and at x = 500?

(a)

To determine

The monthly charge of electricity if 1100kWh of electricity is consumed in a month if the monthly charges for x-kilowatt-hours (kWh) of electricity that is used by a residential consumer of Excelsior Electric Membership Corporation, from November to June.

Explanation

Given Information:

The function,

C(x)={20+0.188x                     if      0x10038.80+0.15(x100)     if      100<x50098.80+0.10(x500)     if      x>500

Consider the provided function,

C(x)={20+0.188x                     if      0x10038

(b)

To determine

To calculate: The values of the limits, limx100C(x) and limx500C(x) if the monthly charges for x-kilowatt-hours (kWh) of electricity that is used by a residential consumer of Excelsior Electric Membership Corporation, from November to June.

(c)

To determine

Whether the function, C(x)={20+0.188x                     if      0x10038.80+0.15(x100)     if      100<x50098.80+0.10(x500)     if      x>500, is continuous at x=100 and x=500 if the monthly charges for x-kilowatt-hours (kWh) of electricity that is used by a residential consumer of Excelsior Electric Membership Corporation, from November to June.

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