Answered: The toll T charged for driving on a…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.2: Graphs Of Functions

Problem 83E: Postage Rates The 2014 domestic postage rate for first class letters weighing 3.5 oz or less is 49...

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Question

The toll T charged for driving on a certain stretch of a toll road is $3 except during rush hours (between 7 a.m. and 10 a.m. and between 4 p.m. and 7 p.m.) when the toll is $5.

(a)

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

(b)

Discuss the discontinuities of of this function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

t =

Classify the discontinuities as removable, jump, or infinite.

removablejump infinitenone — T is continuous

Discuss the significance of the discontinuities of this function to someone who uses the road.

The function is continuous, so there is no significance.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 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 = 0 and t = 7, between t = 10 and t = 16, and between t = 19 and t = 24 if feasible.

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