Concept explainers
The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003 the number of reported cases could be approximated by
t days after March 17, 2003 (the first day for which statistics were reported by the World Health Organization).
a. What was the average rate of change of
b. Which of the following is true? For the first 20 days of the epidemic, the number of reported cases
(A) increased at a faster and faster rate.
(B) increased at a slower and slower rate.
(C) decreased at a faster and faster rate.
(D) decreased at a slower and slower rate. [HINT: See Example 2.]
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Applied Calculus
- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forwardUsing the data in Table 1 at the beginning of this section, find the average rate of change between 2005 and 2010.arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward
- The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?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_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forward
- The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?arrow_forwardUse the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forwardEstimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.arrow_forward
- Molars 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_forwardaThe 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_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning