Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Relativistic Time A correctly functioning hourglass on board a rocket ship would appear to a stationary observer to take longer than an hour to empty. The graph in Figure
a. Use the graph to estimate the value of
c. Does a small change in velocity cause a greater change in apparent time at slower speeds or at faster speeds?
FIGURE 1.50 Relativistic length of an hour
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The Rock with a Changed Reference Point Make graphs of position and velocity for a rock tossed upward from ground level as it might be viewed by someone standing atop a tall building. Thus, the location of the rock is measured by its distance down from the top of the building.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Tornadoes In OklahomaThe graph in Figure 1.41 shows the number T=T(d) of tornadoes in Oklahoma Fl/EF1 and stronger reported by the National Climatic Data Center. Round your answers to the nearest whole number. a. When were the most tornadoes reported? How many were reported in that year? b. When were the fewest tornadoes reported? How many were reported in that year? c. What was the average yearly rate of decrease in tornadic activity from 2011 to 2012? d. What was the average yearly rate of increase in tornadic activity from 2009 to 2011? e. What was the average yearly rate of change that is, the average yearly rate of total increase or total decrease in tornadic activity from 2009 to 2012? FIGURE 1.41 Tornadoes in Oklahomaarrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Falling with a parachuteWhen an average-sized man with a parachute jumps from an airplane, he will fall S=12.5(0.2t1)+20t feet in t seconds. a.Plot the graph of S versus t over at least the first 10seconds of the fall. b.How far does the parachutist fall in 2seconds? c.Calculate dSdt at 2seconds into the fall and explain what the number you calculated means in practical terms.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Rubber Ball A rubber ball is dropped from the top of a building. The ball lands on concrete and bounces once before coming to rest on the grass. Measure the location of the ball as its distance up from the ground. Make graphs of the location and velocity of the ball.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. t is measured in thousands of years, and C=C(t) is the amount, in grams, of carbon-14 remaining. Carbon-14 unstable radioactive t=Thousandofyears C=Gramsremaining 0 5 5 2.73 10 1.49 15 0.81 20 0.44 a. What is the average yearly rate of change of carbon-14 during the first 5000 years? b. How many grams of carbon-14 would you expect to find remaining after 1236 years? c. What would you expect to be the limiting value of C?arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Wind ChillThe graph in Figure 1.40 shows the temperature T = Tv adjusted for wind chill as a function of the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The adjusted temperature T shows the temperature that has an equivalent cooling power when there is no wind. a. At what wind speed is the temperature adjusted for wind chill equal to 0? b. Your answer in part a is the solution of an equation involving Tv. Which equation? c. At what value of v would a small increase in v have the greatest effect on Tv? In other words, at what wind speed could you expect a small increase in wind speed to cause the greatest change in wind chill? Explain your reasoning. d. Suppose the wind speed is 45 miles per hour. Judging from the shape of the graph, how significant would you expect the effect on Tv to be if the wind speed increased? FIGURE 1.40 Temperature adjusted for wind chill when the thermometer reads 30 degrees Fahrenheit.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. World Copper Production World production of copper, in millions of tons per year, from 1900 to 2000 is given by C=0.51.033t, where t is the time in years since 1900. a.What production level does this model give for the year 2000? b.If this model were extended to 2025, how could you use your knowledge of copper production in 2024 to estimate copper production in 2025?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Cleaning Contaminated Water A tank of water is contaminated with 60 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped into tank, and the well-mixed overflow is being collected for removal to a toxic-waste site. The result is that at the end of each hour, there is 22 less salt in the tank than at the beginning of the hour. Let S=S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins. a. Explain why S is an exponential function and find its hourly decay factor. b. Give a formula for S. c. Make a graph of S that shows the flushing process during the first 15 hours, and describe in words how the salt removal process progresses. d. In order to meet EPA standards, there can be no more than 3 pounds of salt in the tank. How long must the process continue before EPA standards are met? e. Suppose this cleanup procedure costs 8000 per hour to operate. How much does it cost to reduce the amount of salt from 60 pounds to 3 pounds? How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. The Photic Zone This is a continuation of Exercise 18. In the ocean, the photic zone is the region where there is sufficient light for photosynthesis to occur. See Figure 4.12. For marine phytoplankton, the photic zone extends from the surface of the ocean to a depth where the light intensity is about 1 of surface light. Near Cape Cod, Massachusetts, the depth of the photic zone is about 16meters. In waters near Cape Cod, by what percentage does light intensity decrease for each additional meter of depth?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Cold Front At 4P.M. on a winter day, an arctic air mass moved from Kansas into Oklahoma, causing temperatures to plummet. The temperature T=T(h) in degrees Fahrenheit h hours after 4P.M. in Stillwater, Oklahoma, on that day is recorded in the following table. h=Hourssince4P.M. T=Temperature 0 62 1 59 2 38 3 26 4 22 a. Use functional notation to express the temperature in Stillwater at 5:30P.M., and then estimate its value. b. What was the average rate of change per minute in temperature between 5P.M. and 6P.M.? What was the average decrease per minute over that time interval? c. Estimate the temperature at 5:12P.M. d. At about what time did the temperature reach the freezing point? Explain your reasoning.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Making Up a Story about a Car TripYou begin from home on a car trip. Initially your velocity is a small positive number. Shortly after you leave, your velocity decreases momentarily to zero. Then it increases rapidly to a large positive number and remains constant for this part of the trip. After a time, your velocity decreases to zero and then changes to a large negativc number. a. Make a graph of velocity for this trip. b. Discuss your distance from home during this driving event, and make a graph. c. Make up a driving story that matches this description.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning