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Cell Sites A cell site is a site where electronic communication equipment is placed in a cellular network for the use of mobile phones. The number
Where t represents the year, with
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Chapter 3 Solutions
Precalculus (MindTap Course List)
- 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_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_forwardBaking a Potato: A potato is placed in a preheated oven to bake. Its temperature P=P(t) is given by P=400325et/50, Where P is measured in degrees Fahrenheit and t is the time in minutes since the potato was placed in the oven. a. Make a graph of P versus t.Suggestion: in choosing your graphing window, it is reasonable to look at the potato over no more than a 2-hour period. After that, it will surely be burned to a crisp. You may wish to look at a table of values to select a vertical span. b. What was the initial temperature of the potato? c. Did the potatos temperature rise more during the first 30 minutes or second 30 minutes of baking? What was the average rate of change per minute during the first 30 minutes? What was the average rate of change per minute during the second 30 minutes. d. Is this graph concave up or concave down? Explain what that tells you about how the potato heats up, and relate this to part c.. e. The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. f. What is the temperature of the oven? Explain how you got your answer. Hint: if the potato were left in the oven for a long time, its temperature would match that of the oven.arrow_forward
- A Cup of Cofee The temperature C of a fresh cup of coffee t minutes after it is poured is given by C = 125e-0.03t 75 degree Fahrenheit. a. Make a graph of Cversus t. b. The coffee is cool enough to drink when its temperature if 150 degrees. When will the coffee be cool enough to drink? c. What is the temperature of the coffee in the pot? Note :We are assuming that the coffee pot is being kept hot and its the same temperature as the cup of coffee when it was poured. d.What is the temperature in the room where you are drinking the coffee? Hint: If the coffee is left to cool a long time, it will reach room temperature.arrow_forwardLidocaine Lidocaine is a drug used to treat irregular heartbeats. After an injection of a 100-mg dose of lidocaine, the amount of the drug in a patients bloodstream is 33.67(e0.0075731te0.12043t)mg at time t minutes after the injection. a. Make a graph of the amount of drug in the bloodstream for t up to 4 hours 240 minutes. b. When does the drug reach its maximum level in the bloodstream? c. For a person of typical size, the drug is effective as long as the amount in the bloodstream is at least 7.5 mg. For how long is the drug at or above that level? Hint: The drug is at that level twice. d. For a person of typical size, the lethal level occurs when the amount in the bloodstream exceeds 30 mg. Is this dose lethal for such a person? e. For a small person, the lethal level occurs when the amount in the bloodstream exceeds 15 mg. Is this dose lethal for such a person? If so, after how many minutes will it be lethal?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_forwardMonthly Payment for a Home: If you borrow 120,000 at an APR of 6 in order to buy a home, and if the lending institution compounds interest continuously, then your monthly payment M=M(Y), in dollars, depends on the number of years Y you take to pay off the loan. The relationship is given by M=120,000(e0.0051)1e0.06Y. a. Make a graph of M versus Y. in choosing a graphing window, you should note that a home mortgage rarely extends beyond 30 years. b. Express in functional notation your monthly payment if you pay off the loan in 20 years, and then use the graph to find that value. c. Use the graph to find your monthly payment if you pay off the loan in 30 years. d. From part b to part c of this exercise, you increased the debt period by 50. Did this decrease your monthly payment by 50? e. Is the graph concave up or concave down? Explain your answer in practical terms. f. Calculate the average decreases per year in your monthly payment from a loan period of 25 to a loan period of 30 years.arrow_forwardSales The sales S (in millions of dollars) for Jazz Pharmaceuticals for the years 2006 through 2014 can be approximated by the model S=27.215t2409.06t+1563.6,6t14 where t represents the year, with t=6 corresponding to 2006. (a) sketch a graph of the model. (b) use the graph to estimate the year in which the sales were $200 million.arrow_forward
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