Concept explainers
Population 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
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) Find 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?
Want to see the full answer?
Check out a sample textbook solutionChapter P Solutions
Trigonometry (MindTap Course List)
- The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?arrow_forwardDoes the following table represent a linear function ? If so, find the linear equation that models the data.arrow_forwardThe U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data forseveral years is given in Table 4[14]. Determine whether the trend appears linear. If so, and assuming the trendcontinues. in what year will the percentage exceed 35%?arrow_forward
- Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forwardHigh School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardWhat is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forward
- Rage of decrease The price of computers has been dropping steadily for the past ten years. If a desktop PC cost 6700 ten years ago, and the same computing power cost 2200 three years ago, find the average rate of decrease per year. Assume a straight-line model.arrow_forwardThe half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning