Concept explainers
Olympic 5000-Meters The accompanying graph shows the winning time (in minutes) at the Olympic Games from 1952 to 2016 for the men's 5000-meterrun, together with a linear approximation of these data. (Data from: The WorldAlmanac and Book of Facts: 2017.)
The equation for the linear approximation is
Cocoa Production In 2005, global cocoa bean production was approximately 3.3 million metric tons. In 2015, production wasapproximately 4.1 million metric tons. (Data from: The Wall StreetJournal.)
a. Write a linear equation expressing cocoa bean production y in terms of the number of years x after 2000.
b. What was the cocoa bean production in 2012?
c. If the trend continues, what will be the first full year in which cocoa bean production exceeds 5 million metric tons?
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- The number y (in thousands) of male participants in high school lacrosse in the United States from 2008 through 2015 can be approximated by the linear model y=3.66t+91.4,2t5 where t represents the year, with t=0 corresponding to 2010. (a) Find algebraically and interpret the y-intercept of the graph of the linear model. (b) Use the linear model to predict the year in which there will be 128,000 male participants.arrow_forwardNeurology The average weight of a male child’s brain is 970 grams at age 1 and 1270 grams at age 3. (a) Assuming that the relationship between brain weight y and age t is linear, write a linear model for the data. (b) What is the slope and what does it tell you about brain weight? (c) Use your model to estimate the average brain weight at age 2. (d) Use your school’s library, the Internet, or some other reference source to find the actual average brain weight at age 2. How close was your estimate? (e) (d) Do you think your model could be used to determine the average brain weight of an adult? Explain.arrow_forwardPharmacology The numbers of prescriptions P (in thousands) filled at two pharmacies from 2012 through 2016 are shown in the table. (a) Use a graphing utility to create a scatter plot of the data for pharmacy A and find a linear model. Let t represent the year, with t=12 corresponding to 2012. Repeat the procedure for pharmacy B. (b) Assume that the models in part (a) can be used to represent future years. Will the number of prescriptions filled at pharmacy A ever exceed the number of prescriptions filled at pharmacy B? If so, when?arrow_forward
- Life Expectancy The average life expectancy in the United States has been rising steadily over the past few decades, as shown in the table. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Use the linear model you found in part (b) to predict the life expectancy in the year 2006. (d) Search the Internet or your campus library to find the actual 2006 average life expectancy. Compare to your answer in part (c).arrow_forwardDemand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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