Answered: The toll T charged for driving on a…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 5SC

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Question

The toll T charged for driving on a certain stretch of a toll road is $2 except during rush hours (between 7 AM and 10 AM and between 4 PM and 7 PM) when the toll is $4.

(a) Sketch a graph of T as a function of the time t, measured in hours past midnight.

(b) Locate the discontinuities of T. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
t =

c)Classify the discontinuities as removable, jump, or infinite.

removable jump infinite none — T is continuous

d)Discuss the significance of the discontinuities of T to someone who uses the road. which is true?

-Because of the steady increases and decreases in the toll, drivers may want to avoid the highest rates at t = 7 and t = 24 if feasible.

-Because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 7 and t = 10 and between t = 16 and t = 19 if feasible.

- Because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 0 and t = 7, between t = 10 and t = 16, and between t = 19 and t = 24 if feasible.

-The function is continuous, so there is no significance.

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