   Chapter 9.1, Problem 68E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Airport parking The Hourly Parking Garage at BWI International Airport in Baltimore costs $2 per half hour during the first hour and$4 for each hour or part of an hour for more than 1 hour and up to 5 hours. If C = C ( t ) is the total charge for t hours in BWI’s Hourly Parking Garage, write a piecewise function that describes C ( t ) for t <   3 . Use C ( t ) to find the following limits, if they exist.(a) lim t → 0.5 − C ( t ) (b) lim t → 0.5 + C ( t ) (c) lim t → 0.5 C ( t ) (d) lim t → 2.5 C ( t )

(a)

To determine

To calculate: The value of the limit limt0.5C(t) using the function describing the total charge for t hours for BWT’s Hourly Parking Garage.

Explanation

Given Information:

The hourly Parking Garage at BWI International Airport in Baltimore costs $2 per half hour during the first hour and$4 each hour or part of an hour for more than 1 hour and up to 5 hours.

The total charge is given by C=C(t), for t<3. The limit is limt0.5C(t).

Formula used:

For a polynomial function f(x)=anxn+an1xn1++a1x+a0 where an0 and n is a positive integer,

limxcf(x)=f(c)

This is defined for all values of c.

Calculation:

Consider the function, C=C(t), to model the total charges, where t is the number of hours.

The hourly Parking Garage at BWI International Airport in Baltimore costs $2 per half hour during the first hour and$4 each hour or part of an hour for more than 1 hour and up to 5 hours

(b)

To determine

To calculate: The value of the limit limt0.5+C(t) using the function describing the total charge for t hours for BWT’s Hourly Parking Garage.

(c)

To determine

To calculate: The value of the limit limt0.5C(t), using the function describing the total charge for t hours for BWT’s Hourly Parking Garage.

(d)

To determine

To calculate: The value of the limit limt2.5C(t) using the function describing the total charge for t hours for BWT’s Hourly Parking Garage.

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