Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
TravelIng in a Car Make graphs of location and velocity for each of the following driving events. In each case, assume that the car leaves from home moving west down a straight road and that position is given as the distance west from home.
a. A vacation: Being eager to begin your overdue vacation, you set your cruise control and drive faster than you should to the airport. You park your car there and get on an airplane to Spain. When you fly back 2 weeks later, you are tired, and you drive back home at a leisurely pace. (Note: Here we are talking about the location of your car, not of the airplane.)
b. On a country road: A car driving down a country road encounters a deer. The driver slams on the brakes, and the deer runs away. The journey is cautiously resumed.
c. At the movies: In a movie chase scene, our hero is driving his car rapidly toward the bad guys. When the danger is spotted, he does a Hollywood 180-degree turn and speeds off in the opposite direction.
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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. 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_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. 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_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. Moores Law The speed of a computer chip is closely related to the number of transistors on the chip, and the number of transistors on a chip has increased with time in a remarkably consistent way. In fact, in the year 1965, Dr. Gordon E. Moore now chairman emeritus of Intel Corporation observed a trend and predicted that it would continue for a time. His observation, now known as Moores law, is that every two years or so a chip is introduced with double the number of transistors of its fastest predecessor. This law can be restated in the following way: If time increases by 1year, then the number of transistors is multiplied by 100.15.More generally, the rule is that if time increases by tyears, then the number of transistors is multiplied by 100.15t.For example, after 8years, the number of transistors is multiplied by 100.158, or about 16. The 6th generation Core processor was released by Intel Corporation in the year 2015. a.If a chip were introduced in the year 2022, how many times the transistors of the 6th generation Core would you expect it to have? Round your answer to the nearest whole number. b.The limit of conventional computing will be reached when the size of a transistors on a chip will be 200 times that of the 6th generation Core. When, according to Moores law, will that limit be reached? c.Even for unconventional computing, the law of physics impose a limit on the speed of computation. The fastest speed possible corresponds to having about 1040 times the number of transistors as on the 6th generation Core. Assume that Moores law will continue to be valid even for unconventional computing, and determine when this limit will be reached. Round your answer to the nearest century.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Falling with a Parachute If an average-sized man jumps from an airplane with a properly opening parachute, his downward velocity v=v(t), in feet per second, t seconds into the fall is given by the following table. t=Secondsintothefall v=Velocity 0 0 1 16 2 19.2 3 19.84 4 19.97 a. Explain why you expect v to have a limiting value and what this limiting value represents physically. b. Estimate the terminal velocity of the parachutist.arrow_forward
- Reminder 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Yellowfin Tuna Data were collected comparing the weight W, in pounds, of a yellowfin tuna to its length L, in centimeters. These data are presented in the following table. L=Length W=Weight 70 14.3 80 21.5 90 30.8 100 42.5 110 56.8 120 74.1 130 94.7 140 119 160 179 180 256 a. What is the average rate of change, in weight per centimeter of length, in going from a length of 100 centimeters to a length of 110 centimeters? b. What is the average rate of change, in weight per centimeter of length, in going from 160 to 180 centimeters? c. Judging from the data in the table, does an extra centimeter of length make more difference in weight for a small tuna or for a large tuna? d. Use the average rate of change to estimate the weight of a yellowtuna fish that is 167 centimeters long? e. What is the average rate of change, in length per pound of weight, in going from a weight of 179 pounds to a weight of 256 pounds? f. What would you expect to be the length of a yellow tuna weighing 225 pounds?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Male and Female High School Graduates The table below shows the percentage of male and female high school graduates who enrolled in college within 12 months of graduation. Years 1960 1965 1970 1975 Males 54 57.3 55.2 52.6 Females 37.9 45.3 48.5 49 a. Find the equation of the regression line for percentage of male high school graduates entering college as a function of time. b. Find the equation of the regression line for percentage of female high school graduates entering college as a function of time. c. Assume that the regression lines you found in part a and part b represent trends in the data. If the trends persisted, when would you expect first to have seen the same percentage of female and male graduates entering college? You may be interested to know that this actually occurred for the first time in 1980. The percentages fluctuated but remained very close during the 1981s and 1990s. In the 2000s, more female graduates entered college than did males. In 2008, for example, the rate for males was 66 compared with 72 for females.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Quarterly Pine Pulpwood PricesIn southwest Georgia, the average pine pulpwood prices vary predictably over the course of the year, primarily because of weather. Prices in 2009 followed this pattern. At the beginning of the first quarter, the average price P was 9 per ton. During the first quarter, prices declined steadily to 8 per ton, then remained steady at 8 per ton through the end of the third quarter. During the fourth quarter, prices increased steadily from 8 to 10 per ton. a.Sketch a graph of pulpwood prices as a function of the quarter in the year. b.What formula for price P as a function of t, the quarter, describes the price from the beginning of the year through the first quarter? c.What formula for price P as a function of t, the quarter, describes the price from the first to the third quarter? d.What formula for price P as a function of t, the quarter, describes the price from the third to the fourth quarter? e.Write a formula for price P throughout the year as a piecewise-defined function of t, the quarter.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Surveying Vertical CurvesWhen a road is being built, it usually has straight sections, all with the same grade, that must be linked to each other by curves. By this we mean curves up and down rather than side to side, which would be another matter. Its important that as the road changes from one grade to another, the rate of change of grade between the two be constant. The curve linking one grade to another grade is called a vertical curve. Surveyors mark distances by means of stations that are 100feet apart. To link a straight grade of g1 to a straight grade of g2, the elevations of the stations are given by y=g2g12Lx2+g1x+Eg1L2. Here y is the elevation of the vertical curve in feet, g1 and g2 are percents, L is the length of the vertical curve in hundreds of feet, x is the number of the station, and E is the elevation in feet of the intersection where the two grades would meet.See Figure 5.72. The station x=0 is the very beginning of the vertical curve, so the station x=0 lies where the straight section with grade g1 meets the vertical curve. The last station of the vertical curve is x=L, which lies where the vertical curve meets the straight section with grade g2. Figure 5.72 Assume that the vertical curve you want to design goes over a slight rise, joining a straight section of grade 1.35 to a straight section of grade 1.75. Assume that the length of the curve is to be 500feet so L=5 and that the elevation of the intersection is 1040.63feet. a.What is the equation for the vertical curve described above? Dont round the coefficients. b.What are the elevations of the stations for the vertical curve? c.Where is the highest point of the road on the vertical curve? Give the distance along the vertical curve and the elevation.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning