Concept explainers
Population Model The following data represent the population of the United States. An ecologist is interested in building a model that describes the population of the United States.
Source: U.S. Census Bureau
Using a graphic utility, draw a
Using a graphic utility, build a logistic model from the data.
Using a graphic utility, graph the function found in part (b) on the scatter plot.
Based on the function found in part (b), what is the carrying capacity of the United States?
Use the function found in part (b) to predict the population of the United States in
When will the United States population be
Compare actual U.S. Census figures to the predictions found in parts (e) and (f). Discuss any differences.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
Precalculus: A Unit Circle Approach
Precalculus: A Unit Circle Approach (3rd Edition)
- Oil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forwardEnergy ConsumptionThe monthly residential consumption of energy in the U.S. for 2012 is found in the following table. Source: Energy Information Administration. Month Energytrillion BTU January 990.527 February 833.163 March 560.826 April 412.426 May 297.500 June 253.015 July 240.486 August 248.035 September 249.354 October 378.094 Number 631.203 December 838.265 Plot the data, letting t=1 correspond to January, t=2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic? Find the trigonometric function of the form C(t)=asin(bt+c)+d that models these data when t is the month of the year and C(t) is the energy consumption. Graph the function on the same calculator window as the data. Estimate the total energy consumption for the year for residential customers in the United States and compare it to the actual value. Calculate the period of the function found in part b. Is this period reasonable?arrow_forwardLIFE SCIENCE APPLICATIONS Body Surface Area The surface area of a human in square meters has been approximated by A(h,m)=0.024265h0.3964m0.5378, where h is the height in cm and m is the mass in kg. Find A for the following data. Source: The Journal of Pediatrics. a. Height, 178cm; mass, 72kg b. Height, 140cm; mass 65kg c. Height, 160cm; mass, 70kg d. Using your mass and height, find your own surface area. e. f.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill