Reminder Round all answers to two decimal places unless otherwise indicated.
Waiting at a Stop Sign Consider a side road connecting to a major highway at a stop sign. According to a study by D.R. Drew, the average delay
where
a. What is the average delay time if the flow rate is
b. The service rate
Use function composition to represent the service rate as a function of flow rate. Reminder:
c. What flow rate will permit a stop sign service rate of
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
EBK FUNCTIONS AND CHANGE: A MODELING AP
- aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).arrow_forwardMass of Bighorn Yearlings The body mass of yearling bighorn sheep on Ram Mountain in Alberta, Canada, can be estimated by M(t)=27.5+0.3t0.001t2 Where M(t) is measured in kilograms and t is days since May 25. Source: Canadian Journal of zoology. a. Find the average rate of change of the mass of bighorn yearling between 105 and 115 days past May 25. b. Find the instantaneous rate of change of the mass for a bighorn yearling sheep whose age is 105 days past May 25. c. Graph the function M(t) on [5,125] by [25,65]. d. Does the behavior of the function past 125 days accurately model the mass of the sheep? Why or why not? e. f. g.arrow_forwardMobile Phone Sales In 2000, mobile handset sales totaled 414.99million. In 2005, the total was 778.75million. Let M=M(t) denote total mobile handset sales in year t. What was the average rate of change per year in M(t) from 2000 to 2005? Be sure to include proper units with your answer.arrow_forward
- A 500-mg dose of a drug is administered by rapid injection to a patient. The half-life of the drug is 9 hours. a. Find a model for the amount of drug in the bloodstream t hours after the drug is administered. b. Find the average rate of change of drug in the bloodstream between t=0 and t=2. Repeat for t=9 and t=11.arrow_forwardVelocity A car is moving along a straight test track. The position in feet of the car, s(t), at various times t is measured, with the following results. Find and interpret the average velocities for the following changes in t. a. 0to2seconds b. 2to4seconds c. 4to6seconds d. 6to8seconds e. Estimate the instatneous velocity at 4 seconds. i. by finding the average velocity between 2 and 6 seconds, and ii. by averageing the answers for the average velocity in the two seconds before and the two seconds after that is, the answers to parts b and c. f. Estimate the instantaneous velocity at 6 seconds using the two methods in part e. g. Notice in parts e and f that your two answers are the same. Discuss whether this will always be the case, and why or why not.arrow_forwardMolars The crown length as shown below of first molars in fetuses is related to the postconception age of tooth as L(t)=0.01t2+0.788t7.048, Where L(t) is the crown length, in millimeters, of the molar t weeks after conception. Source: American Journal of Physical Anthropology. a. Find the average rate of growth in crown length during weeks 22 through 28. b. Find the instantaneous rate of growth in crown length when the tooth is exactly 22 weeks of age. c. Graph the function on [0,50] by [0,9]. Does a function that increases and then begins to decrease make sense for this particular application? What do you suppose is happening during the first 11 weeks? Does this function accurately model crown length during those weeks?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning