Reminder Round all answers to two decimal places unless otherwise indicated.
Grains of Wheat on a Chess Board A children’s fairy tale tells of a clever elf who extracted from a king the promise to give him one grain of wheat on a chess board square today, two grains on an adjacent square tomorrow, four grains on an adjacent square the next day, and so on, doubling the number of grains each day until all 64 squares of the chess board were used. How many grains of wheat did the hapless king contract to place on the
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Chapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. An Expensive Book A scientist visited Amazon.com to purchase a book. To his amazement, he found the book priced at 23,698,655.93. He discovered that there were two vendors selling this book on Amazon, and each was using a computer to adjust the price based on the other sellers price. The result was that each day the first vendors price was multiplied by 1.27. Assume that the initial price was 134.27, and determine how many days it took for the first vendors price to reach the exorbitant figure above. Round your answer to the nearest day.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Recent EarthquakesOn April 25, 2015, an earthquake of magnitude 7.8 on the Richter scale struck Nepal. On May 12, 2015, a major aftershock of magnitude 7.3 on the Richter scale shook the same region. a. How did the power of the first earthquake and this aftershock compare? b. What would be the magnitude of a quake twice as powerful as the first quake?arrow_forwardReminder 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_forward
- Reminder 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. 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. State QuakesThe largest recorded earthquake centered in Idaho measured 7.2 on the Richter scale. a. The largest recorded earthquake centered in Montana was 3.16 times as powerful as the Idaho earthquake. What was the Richter scale reading for the Montana earthquake? b. The largest recorded earthquake centered in Arizona measured 5.6 on the Richter scale. How did the power of the Idaho quake compare with that of the Arizona quake?arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Digitized Pictures on a Disk Drive The hard disk drive on a computer holds 800 gigabytes of information. That is 800,000 megabytes. The formatting information, operating system, and applications software take up 6000 megabytes of disk space. The operator wants to store on his computer a collection of digitized pictures, each of which requires 2 megabytes of storage space. a. We think of the total amount of storage space used on the disk drive as a function of the number of pictures that are stored on the drive. Explain why this function in linear. b. Find a formula to express the total amount of storage space used on the disk drive as a linear function of the number of pictures that are stored on the drive. Be sure to identify what the letters you use mean. Explain in practical terms what the slope of this function is. c. Express using functional notation the total amount storage space used on the disk drive if there are 350 pictures stored on the drive, and then calculate that value. d. After putting a number of pictures on the disk drive, the operator executes a directory command, and at the end of the list, the computer displays the message 769, 000, 000, 000 bytes free. This message means that there are 769,000 megabytes of storage space left on the computer. How many pictures are stored on the disk drive? How many additional pictures can be added before the disk drive is filled?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Sleeping Longer A certain man observed that each night he was sleeping 15 minutes longer than he had the night before, and he used this observation to predict the day of his death. 9 If he made his observation right after sleeping 8 hours, how long would it be until he slept 24 and so would never again wake?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Earthquakes in Alaska and ChileIn 1964, an earthquake measuring 9.2 on the Richter scale occurred in Alaska. a. How did the power of the New Madrid earthquake described in Example 4.12 compare with that of the 1964 Alaska earthquake? b. In 1960 an earthquake occurred in Chile that was 2 times as powerful as the Alaska quake. What was the Richter scale reading for the Chilean earthquake? EXAMPLE 4.12COMPARING SOME FAMOUS EARTHQUAKES On December 16, 1811, an earthquake occurred near New Madrid, Missouri, that temporarily reversed the course of the Mississippi River. This was actually one of a series of earthquakes in the area, one of which is estimated to have had a Richter magnitude of 8.8.The area was sparsely populated at the time, and there were thought to be few fatalities. On October 17, 1989, a calamitous earthquake measuring 7.1 on the Richter scale occurred in the San Francisco Bay area. The earthquake killed 67 and injured more than 3000. Part 1How much more powerful was the New Madrid quake than the 1989 San Francisco quake? Part 2If an earthquake 1000 times as powerful as the 1989 San Francisco earthquake occurred, what would its Richter scale measurement be? Part 3On December 26, 2004, an earthquake 2 times as powerful as the New Madrid quake struck the Indian Ocean near Indonesia. It caused a tsunami that resulted in the deaths of hundreds of thousands. What was the Richter scale reading for this quake?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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Insect ControlDDT dichlorodiphenyltrichloroethane was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 100 kilograms of DDT that has seeped into the soil. t=time,inyearssinceapplication D=DDTremaining,inkilograms 0 100.00 1 95.00 2 90.25 3 85.74 a. Show that the data are exponential. b. Make a model of D as an exponential function of t. c. What is the half-life of DDT in the soil? That is, how long will it be before only 50 kilograms of DDT remain?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Renting Motel Rooms You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for 85.00, two for 83.00 each, and in general the group rate per room is found by taking 2 off the base of 85 for each extra room rented. a.How much money do you charge per room if a group rents 3 rooms? What is the total amount of money you take in? b.Use a formula to give the rate you charge for each room if you rent n rooms to an organization. c.Find a formula for a function R=R(n) that gives the total revenue from renting n rooms to a convention host. d.Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate that value.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning