Population The population
(a) Graphically estimate the
(b) Find algebraically and interpret the
(c) Use the model to predict the year in which the population will be 538,000. Does your answer seem reasonable? Explain.
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Chapter 1 Solutions
College Algebra
- Population The population y (in thousands) of Buffalo, New York, from 2000 to 2014 can be approximated by the model y=2.60t+291.7,0t14, where t represents the year, with t=0 corresponding to 2000 (see figure). (a) Graphically estimate the y-intercept of the graph. (b) Find algebraically and interpret the y-intercept of the graph. (c) Use the model to predict the year in which the population will be 239,000. Does your answer seem reasonable? Explain.arrow_forwardProjectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?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_forward
- 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?arrow_forwardRevenue The revenue R (in millions of dollars) for a construction company from 2003 through 2010 can be modeled by R=0.1104t45.152t3+88.20t2654.8t+1907,7t16 where t represents the year, with t=7 corresponding to 2007. (a) Use a graphing utility to approximate any relative minima or maxima of the model over its domain. (b) Use the graphing utility to approximate the intervals on which the revenue for the company is increasing and decreasing over its domain. (c) Use the results of parts (a) and (b) to describe the company’s revenue during this time period.arrow_forwardRevenue The revenue R (in millions of dollars) for a software company from 2003 through 2016 can be modeled by R=6.212t3152.87t2+990.2t414,3t16 where t represents the year, with t=3 corresponding to 2003. (a) Use a graphing utility to approximate any relative minima or maxima of the model over its domain. (b) Use the graphing utility to approximate the intervals on which the revenue for the company is increasing and decreasing over its domain. (c) Use the results of parts (a) and (b) to describe the company’s revenue during this time period.arrow_forward
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