Concept explainers
Cell Sites A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2014 can be modeled by
where
(a) Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.
(b) Use a graphing utility to graph the function.
(c) Use the graph to determine the year in which the number of cell sites reached 270,000.
(d) Confirm your answer to part (c) algebraically
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Chapter 5 Solutions
College Algebra
- 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,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_forwardStopping distance, The stopping distance of an automobile is the distance travelled during the driver’s reaction time plus the distance travelled after the driver applies the brakes. In an experiment, researchers measured these distances (in feet) when the automobile was traveling at a speed of x. miles per hour on dry, level pavement, as shown in the bar graph. The distance travelled during the reaction time R was R=1.1x and the braking distance B was B=0.0475x20.001x+0.23. (a) Determine the polynomial that represents the total stopping distance T. (b) Use the result of part (a) to estimate the total stopping distance when x=30,x=40, andx=55 miles per hour. (c) Use the bar graph to make a statement about the total stopping distance required forincreasing speeds.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,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_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 The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by the model y=11.09t+293.4,0t14, 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 538,000. Does your answer seem reasonable? Explain.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
- 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?arrow_forwardMeasurement Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters y to gallons x. Then use the model to find the numbers of liters in 5 gallons and 25 gallons.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_forward
- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardConstruction Costs The town of Foxton lies 10 mi north of an abandoned east-west road that runs through Grimley, as shown in the figure. The point on the abandoned road closed to Foxton is 40 mi from Grimley. Country officials are about to build a new road connecting the two towns. They have determined that restoring the old road would cost 100,000 per mile, while building a new road would cost 200, 000 per mile. How much of the abandoned road should be used as indicated in the figure if the officials intend to spend exactly 6.8 million? Would it cost less than this amount to build a new road connecting the towns directly?arrow_forwardTravel Time You are driving on a Canadian freeway to a town that is 500 kilometers from your home. After 30 minutes, you pass a freeway exit that you know is 50 kilometers from your home. Assuming that you continue at the same constant speed, how long does the entire trip take?arrow_forward
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