Reminder Round all answers to decimal places unless otherwise indicated.
Hiking You are hiking in a hilly region, and
a. Explain the meaning of
b. Where might you be when
c. You reach a point where
d. Where might you be when
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to decimal places unless otherwise indicated. Investing in the Stock Market You are considering buying three stocks whose prices at time t are given by P1(t),P2(t)andP3(t) . You know that dP1dt is a large positive number, dP2dt is near zero, and dP3dt is a large negative number. Which stock will you buy? Explain your answer.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Ship Propellers An ideal diameter d, in feet, of a ships propeller is given by the formula d=ch1/5r3/5. Here h is the horsepower of the engine driving the propeller. r is the maximum number of revolutions per minute of the propeller, and c is a constant. In both parts, give your answer in terms of a percentage. a. If the horsepower is increased by 20 while the number of revolutions per minute remains the same, how is the propeller diameter affected? b. If the horsepower remains the same while the number of revolutions per minute is increased by 20, how is the propeller diameter affected?arrow_forward
- Reminder 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 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Wrap Skirt Figure 3.13 shows a simplified pattern for a wrap skirt that is 20 inches long. The bottom hem for this pattern has a length of 63 inches. Suppose you decide to alter the pattern to make a skirt that is 24 inches long. What should be the length of the bottom hem?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Falling Objects An object is dropped near the surface of a planet. The time T, in seconds, it takes for the object to falls feet is given by the formula T=cs0.5 for some constant c that depends on the planet. a. On Earth, the constant c is 0.25. How long does it take an object to fall 16feet on Earth? b. On a certain planet, an object takes 5seconds to fall 20feet. What is the value of the constant c for this planet? c. If it takes 1second for an objects to fall 10feet on a planet, how long does it take an object to fall 40feet?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_forwardReminderRound all answers to two decimal places unless otherwise indicated. NoteSome of the formulas below use the special number e, which was presented in the Prologue. Sound Pressure and DecibelsSounds exerts a pressure P on the human ear. This pressure increases as the loudness of the sound increases. If the loudness D is measure in decibels and the pressure P is measured in dynes per square centimeter, then the relationship is give by P=0.00021.122D. a.Ordinary conversation has a loudness of about 65 decibels. What is the pressure exerted on the human ear by ordinary conversation? b.A decibel level of 120 causes pain to the ear and can result in damage. What is the corresponding pressure level on the ear?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. The Fukushima Disaster On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away?' Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram." The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-131 that would remain after t days. t=time,indays I=amountofiodine-131 0 54.00 1 49.52 2 45.41 3 41.64 4 38.18 a. Show that the data are exponential. In this part and the next, round to three decimal places b. Find an exponential model that shows the amount of iodine-131 present after t days. c. How long will it take for the amount of iodine-131 to fall to the government limit of 2 thousand becquerels per kilogram? Round your answer to the nearest whole day.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Airspeed The airspeed of a plane is its speed in the absence of wind. With a headwind, ground speed the actual speed in relation to the ground is decreased by the speed of the wind. With a tailwind, ground speed is increased by the speed of the wind. Let A denote the airspeed of a plane and W the speed of the wind, both in miles per hour. Suppose it takes the plane 9 hours to travel the 720 miles from one town to another facing a headwind of W. the return trip, now with a tailwind of W, takes only 6 hours. a. Express the ground speed on the trip out in terms of A and W. b. Use the information from part a and the fact that distance equals rate times time to find an equation involving A and W for the trip out. c. Express the ground speed on the return trip in terms of A and W. d. Use the information from part c and the fact that distance equals rate times time to find an equation involving A and W for the return trip. e. Find the airspeed and the speed of the wind.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Travel Time The time T, in hours, required to drive 100miles is a function of the average speed s, in miles per hour. The formula is T=100s. a. Make a graph T versus s covering speeds up to 70milesperhour. b. Calculate T(25) and explain in practical terms what your answer means. c. Explain in practical terms the behavior of the graph near the pole at s=0.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning