Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Getting Velocity from a Formula When a man jumps from an airplane with an opening parachute, the distance
a. | Use your calculator to make a graph of
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b. | Sketch a graph of velocity for the first
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Chapter 6 Solutions
FUNCTIONS AND CHANGE COMBO
- Immigration The following graph shows immigrationin thousand to the United States has varied over the past century. Source: Homeland Security. a. Find the average annual rate of change in immigration for the first half of the century from 1905 to 1955. b. Find the average annual rate of change in immigration for the second half of the century from 1955 to 2005. c. Find the average annual rate of change in immigration for the entire century from 1905 to 2005. d. Average your answers to part a and b, and compare the result with your answer from part c. Will these always be equal for any two time periods? e. If the annual average rate of change for entire century continues, predict the number of immigrants in 2009. Compare answer to the actual number of 1,130,818 immigrants.arrow_forwardLIFE SCIENCE APPLICATIONS Pollution Pollution begins to enter a lake at time t=0 at a rate in gallons per hour given by the formula f(t)=10(1e0.5t), where t is the time in hours. At the same time, a pollution filter begins to remove the pollution at a rate g(t)=0.4t as long as pollution remains in the lake. a. How much pollution is in the lake after 12 hours? b. Use a graphing calculator to find the time when the rate that pollution enters the lake equals the rate the pollution is removed. c. Find the amount of pollution in the lake at the time found in part b. d. Use a graphing calculator to find the time when all the pollution has been removed from the lake.arrow_forwardLIFE SCIENCE APPLICATION Shadow Length A man 6 ft tall is walking away from a lamp post at the rate of 50 ft per minute. When the man is 8 ft from the lamp post, his shadow is 10 ft long. Find the rate at which the length of the shadow is increasing when he is 25 ft from the lamp post. See the figure.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_forwardRipples in a pond When a stone is thrown into the center of a pond, the ripples spread out in a circular pattern, moving at a rate of 3 feet per second. If the stone is dropped at a point (0,0) in the illustration, when will the ripple reach the seagull floating at the point (15,36)?arrow_forwardA forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).arrow_forward
- Medical Drugs When a certain medical drug is administered to a patient, the number of milligrams remaining in the patients bloodstream after t hours is modeled by D(t)=50e0.2t How many milligrams of the drug remain in the patients bloodstream after 3 hours?arrow_forwardPhysician Demand The demand for physicians is expected to increase in the future, as shown in the accompanying table. Source: Association of American Medical Colleges. Year Demand for Physicians in thousands 2006 680.5 2015 758.6 2020 805.8 2025 859.3 a. Plot the data, letting t=0 correspond to 2000. Does fitting an exponential curve to the data seem reasonable? b. Use the data for 2006 and 2015, to find the function of the form f(t)=Cekt that goes through these two points. c. Use your function from part b to predict the demand for physicians in 2020 and 2025. How well do these predictions fit the data? d. If you have graphing calculator or computer program with an exponential regression feature, use it to find an exponential function that approximately fits the data. How does this answer compare with answer to part b?arrow_forwardDoctors treated a patient at an emergency room from 2:00P.M. to 7:00P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by L=0.270t2+3.59t+83.1,2t7 where t represents the time of day, with t=2 corresponding to 2:00P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93 .arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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