Concept explainers
Sales The rate of sales of your company’s Jackson Pollock Advanced Paint-by-Number sets can be modeled by
t months after their introduction. Find an expression for the total number of paint-by-number sets
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Finite Mathematics and Applied Calculus (MindTap Course List)
- Voting-Age Population The total voting-age population P (in millions) in the United States from 1990 through 2014 can be modeled by P=184.64+0.7524t21+0.0028t2,0t24 where t represents the year, with t=0 corresponding to 1990. (a) In which year did the total voting-age population reach 210 million? (b) Use the model to predict when the total voting-age population will reach 260 million. Is this prediction reasonable? Explain.arrow_forwardPopulation The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P=57.59e0.0051t, where t represents the year, with t=3 corresponding to 2003. (a) According to the model, is the population of Italy increasing or decreasing? Explain. (b) Find the populations of Italy in 2003 and 2015. (c) Use the model to predict the populations of Italy in 2020 and 2025.arrow_forwardSize of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C=7430.402n+0.00012n2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a. Make a graph of C versus n. b. What enrollment size gives a minimum per-pupil cost? c. If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?arrow_forward
- Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forwardPopulation Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0r70 Where y represents the life expectancy and t is the time in years, with t=0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. (d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explainarrow_forwardFinding mass transit fares The Municipal Transit Authority serves 150,000 commuters daily when the fare is 1.80. Market research has determined that every penny decrease in the fare will result in 1000 new riders. What fare will maximize revenue?arrow_forward
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