Temperature The table shows the normal daily high temperatures for Miami M and Syracuse S (in degrees Fahrenheit) for month t, with t = 1 corresponding to January. (Source: National Oceanic and Atmospheric Administration)
t | 1 | 2 | 3 | 4 | 5 | 6 |
M | 76.5 | 77.7 | 80.7 | 83.8 | 87.2 | 89.5 |
S | 31.4 | 33.5 | 43.1 | 55.7 | 68.5 | 77.0 |
t | 7 | 8 | 9 | 10 | 11 | 12 |
M | 90.9 | 90.6 | 89.0 | 85.4 | 81.2 | 77.5 |
S | 81.7 | 79.6 | 71.4 | 59.8 | 47.4 | 36.3 |
(a) A model for Miami is
M(t) = 83.70 + 7.46 sin(0.4912t –1.95).
Find a model for Syracuse.
(b) Use a graphing utility to plot the data and graph the model for Miami. How well does the model fit?
(c) Use a graphing utility to plot the data and graph the model for Syracuse. How well does the model fit?
(d) Use the models to estimate the average annual temperature in each city. Which term of the model did you use? Explain.
(e) What is the period of each model? Is it what you expected? Explain.
(f) Which city has a greater variability in temperature throughout the year? Which factor of the models determines this variability? Explain.
Trending nowThis is a popular solution!
Chapter P Solutions
Calculus (Looseleaf) - Text Only (Custom)
- Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?arrow_forwardRunning In 1987, Canadian Ben Johnson set a world record in the 100-m sprint.The record was later taken away when he was found to have used an anabolic steroid to enhance his performance. His speed at various times in the race is given in the following table . Source: Information Graphics. Timesec Speedmph 0 0 1.84 12.9 3.80 23.8 6.38 26.3 7.23 26.3 8.96 26.0 9.83 25.7 a. Use the information in the table and left endpoints to estimate the distance that Johnson ran in miles. You will first need to calculate t for each interval. At the end, you will need to divide by 3600 the number of seconds in an hour, since the speed is in miles per hour. b. Repeat part a, using right endpoints. c. Wait a minute, we know that the distance Johnson ran is 100m. Divide this by 1609, the number of meters in a mile, to find how far Johnson ran in miles. Is your answer from part a or part b closer to the true answer? Briefly explain why you think this answer should be more accurate. d.arrow_forwardFind the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt