Concept explainers
Reminder 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
|
|
|
|
|
|
|
|
|
|
|
|
a. Explain why you expect
b. Estimate the terminal velocity of the parachutist.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
Algebra And Trigonometry (11th Edition)
College Algebra (7th Edition)
Glencoe Algebra 2 Student Edition C2014
College Algebra
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
- 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. 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. 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
- Reminder 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_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_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_forward
- Reminder 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. 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 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_forward
- Reminder 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_forwardReminderRound all answers to two decimal places unless otherwise indicated. Protein Content of Wheat GrainProtein content of wheat grain is affected by soil moisture and the amount of available nitrogen among other things. Figure 1.45 shows" the percent of protein content of wheat grain versus pounds of nitrogen per acre applied in three separate situations. In each case, soil moisture refers to moisture at the soil depth of 2 inches to 12 inches. Situation 1: Irrigation was used when soil moisture dropped to 49. Situation 2: Irrigation was used when soil moisture dropped to 34. Situation 3: Irrigation was used when soil moisture dropped to 1. a. If irrigation begins when soil moisture reaches 49, what application of nitrogen will result in the lowest percentage of protein in wheat grain? b. If irrigation begins when soil moisture reaches 34, what application of nitrogen will result in the same protein content of wheat grain as beginning irrigation when soil moisture reaches 1? c. If you irrigate when soil moisture reaches 34, how much nitrogen should you apply to achieve a 13 protein content in wheat grain? d. Does Figure 1.45 indicate that, for nitrogen levels at 45 pounds per acre or higher, increased protein content in wheat grain is associated with higher or lower soil moisture? FIGURE 1.45 Protein content versus availability of nitrogenarrow_forwardReminder Round all answers to decimal places unless otherwise indicated. Mileage for an Old Car The gas mileage M that you get on your car depends on its age t in years. a. Explain the meaning of dMdt in practical terms. b. As your car ages and its performance degrades, do you expect dMdt to be positive or negative?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning