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
Luxury Handbags MichaelKors now dominates the handbag market in North America. In 2011, the company had 5% of the market;in 2015, it had 23%. (Data from: The Wall Street Journal.)
a. Write a linear equation expressing the percentage of the luxury handbag market y that Michael Kors had x years after 2000.
b. What was the percentage of the market that Michael Kors had in 2013?
c. If the trend continues, what will be the first full year in which Michael Kors had 30% of the market?
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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- 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_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_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_forward
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