Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Travel Time The time
a. Make a graph
b. Calculate
c. Explain in practical terms the behavior of the graph near the pole at
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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. Estimating Wave Height Sailors use the following function to estimate wave height h, in feet, from wind speed w, in miles per hour h=0.02w2 a. Make a graph of wave height versus wind speed. Include wind speeds of up to 25 miles per hour. b. A small boat can sail safely provided wave heights are no more than 4 feet. What range of wind speed will give safe sailing for this boat?arrow_forwardReminderRound 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_forwardReminderRound 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_forward
- ReminderRound 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_forwardReminder: Round all answer to two decimal places unless otherwise indicated. 15.Total Cost The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To deter mine a formula for the total cost, we need to know the manufacturers fixed costs covering things such as plant maintenance and insurance, as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of 9000 per month and that the variable cost is 15 per widget so it costs 15 to produce 1 widget. a. Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. Be sure to state the units you use. b. Express using functional notation the total cost if there are 250 widgets produced in a month, and then calculate that value.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. The Rock with a Formula If from ground level we toss a rock upward with a velocity of 30feetpersecond, we can use elementary physics to show that the height in feet of the rock above the ground t seconds after the toss is given by S=30t16t2. a. Use your calculator to plot the graph of S versus t. b. How high does the rock go? c. When does it strike the ground? d. Sketch the graph of the velocity of the rock versus time.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Minimum WageOn July 24, 2008, the federal minimum wage was 6.55perhour. On July 24, 2009, this wage was raised to 7.25perhour. If W(t) denotes the minimum wage, in dollars per hour, as function of time, in years, use the given information to estimate dWdt in 2009.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Sales Growth A study of the sales s, in thousands of dollars, of a product as a function of time t, in years, yields the equation of change dsdt=0.3s(4s). This is valid for s less than 5. a.What level of sales will be attained in the long run? b.What is the largest rate of growth in sales?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. Giants Ants and Spiders Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. Of course, they are in the end defeated by the hero and heroine. biologists use power function as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas the cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed radiation is enlarged to 500 times its normal length. Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction. a.By how much will its weight be increased? b.By how much will the cross-sectional area of its legs be increased? c.Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? What do you think is likely to happen to this unfortunate ant? Note: The factor by which pressure increases is given by . FactorofincreaseinweightFactorofincreaseinarea)arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. InflationDuring a period of high inflation, a political leader was up for re-election. Inflation had been increasing during his administration, but he announced that the rate of increase of inflation was decreasing. Draw a graph of inflation versus time that illustrates this situation. Would this announcement convince you that economic conditions were improving?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning