Concept explainers
A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel,
One analysis (involving additional data) used a cubic equation to model this data.
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Price, dollars per barrel |
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a. Use cubic regression to model these data. Round the regression parameters to four decimal places.
b. Plot the data along with the cubic model.
c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020.
d. What estimate does the model give for oil prices in 2015?
e. The actual price of oil in December of 2015 was about
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forwardLife Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forward
- TEST FOR UNDERSTANDING FOR EXAMPLE 5.16 In the study Economics of Scale in High School Operation by J. Riew, the author studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 enrollment. The data he observed were similar to those in the table below. n=enrollment 200 600 1000 1400 1800 C=costperstudent,indollars 667.4 545.0 461.0 415.4 408.2 Model these data using a quadratic function. Round regression parameters to four decimal places. According to this model, what enrollment produces the minimum cost per student?arrow_forwardTEST YOUR UNDERSTANDING | FOR EXAMPLE 4.11 A small dog will weigh 20pounds at adulthood. The following table shows the weight w, in pounds, of the dog tmonths after birth. The difference D between the maximum weight of 20pounds and the current weight W, in pounds, is recorded in the third row of the table. t=time,inmonths 2 4 7 8 10 W=weight,inpounds 5.0 10.5 15.5 17.0 19.0 D=20-W 15.0 9.5 4.5 3.0 1.0 Find an exponential model for D as a function of t. Use your model for D to give a formula for W in terms of t.arrow_forwardTEST YOUR UNDERSTANDING The following table shows the average price P, in dollars, of a gallon of regular gas t years after 2000. t = year since 2000 0 2 4 7 8 P = price in dollars 1.51 1.36 1.88 2.80 3.27 Find the equation of the regression line for P as a function of t. What price does your model give for gas in 2009? Compute your answer with the actual value of 2.35.arrow_forward
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