Time (months) 012 34 5 Rate pollutants are escaping (tons/month) 2 37 1321 36 Use this data to sketch a smooth curve relating the two variables. Draw rectangles on the graph you drew to help you underestimate the total pollutants that escaped during the first month. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the first month. What overestimate did you obtain? tons Draw rectangles on this graph to help you underestimate the total pollutants that escaped during the whole time. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the whole time. What overestimate did you obtain? tons

Time (months) 012 34 5 Rate pollutants are escaping (tons/month) 2 37 1321 36 Use this data to sketch a smooth curve relating the two variables. Draw rectangles on the graph you drew to help you underestimate the total pollutants that escaped during the first month. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the first month. What overestimate did you obtain? tons Draw rectangles on this graph to help you underestimate the total pollutants that escaped during the whole time. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the whole time. What overestimate did you obtain? tons

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.6: Optimization

Problem 2E: Life Expectancy Versus Health Care Spending One article shows a relationship between per capita...

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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 y=63.6+0.97t1+0.01t,0t70 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?
The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x=0 corresponds to 6 a.m. These data can be approximated by the model y=0.026x31.03x2+10.2x+34,0x24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Life Expectancy Versus Health Care Spending One article shows a relationship between per capita health care spending h, in thousands of U.S. dollars per person per year, and life expectancy E, in years. The following formula is adapted from that article: E=72.23+3.85h0.37h2 We should point out that this article includes no justification for the type of model used. a.Plot the graph E versus h. Include spending levels from 1000 to 9000 per person per year so a horizontal span of 1 to 9. b. According to this model, what health care expenditure corresponds to maximum longevity? Round your answer in thousands of dollars per person per year to two decimal places. c.What optimum life expectancy is given by this model? For comparison, in 2011, in the United States, per capita health care spending was 8745 and life expectancy was 78.7 years.
World Crude Oil Production In 1956, M.King Hubbert proposed a model to analyse crude oil production. His model, with updated data, gives world crude oil production as P=254.43e0.042t(1+2.12e0.042t)2 Here P is measured in billions of barrels per year, and t is time, in year, since 2000. a.Make a graph of world crude oil production for 2000 through 2040. b.When does this model predict a peak in world crude oil production? c.What is the maximum crude oil production predicted by this model?
Constant Velocity When the graph of directed distance is a straight line, what can be said about the graph of velocity?