Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Moore’s 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
a. If a chip were introduced in the year
b. The limit of conventional computing will be reached when the size of a transistors on a chip will be
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
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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. 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_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_forwardReminderRound all answers to two decimal places unless otherwise indicated. HydrographsWhen a rainfall brings more water than the soil can absorb, runoff occurs, and hydrologists refer to the event as a rainfall excess. The easiest way to envision runoff is to think of a watershed that drains into the mouth of a single stream. The runoff is the number of cubic feet per minute cfpm being dumped into the mouth of the stream. An important way of depicting runoff is the hydrograph, which is simply the graph of total discharge, in cubic feet per minute, versus time. A typical runoff hydrograph is shown in Figure 1.47. The horizontal axis is hours since rainfall excess began. A hydrograph displays a number of important features. a. Time to peak is the elapsed time from the start of rainfall excess to peak runoff. What is the time to peak shown by the hydrograph in Figure 1.47? b. Time of concentration is the elapsed time from the end of rainfall excess to the inflection point after peak runoff. The end of rainfall excess is not readily apparent from a hydrograph, but it occurs before the peak. If the end of rainfall excess occurred 5 hours after the start of rainfall excess. estimate the time of concentration from Figure 1.47. c. Recession time is the time from peak runoff to the end of runoff. Estimate the recession time for the hydrograph in Figure 1.47. d. Time base is the time from beginning to end of surface runoff. What is the time base for the hydrograph in Figure 1.47? FIGURE 1.47 A runoff hydrographarrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Inflation The yearly inflation rate tells the percentage by which prices increase. For example, from 1990 through 2000, the inflation rate in the United States remained stable at amount 3 per year. In 1990, an individual retired on a fixed income of 36,000 per year. Assuming that the inflation rate remains at 3, determine how long it will take for the retirement income to deflate to half its 1990 value. Note: To say that retirement income has deflated to half its 1990 value means that prices have doubled.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. The MacArthur-Wilson Theory of Biogeography Consider an island that is separated from the mainland, which contains a pool of potential colonizer species. The MacArthur-Wilson theory of biogeography hypothesizes that some species from the mainland will migrate to the island, but that increasing competition on the island will lead to species extinction. It further hypothesizes that both the rate of migration and the rate of extinction of species are exponential functions, and that an equilibrium occurs when the rate of extinction matches the rate of immigration. This equilibrium point is thought to be the point at which immigration and extinction stabilize. Suppose that, for a certain island near the mainland, the rate of immigration of new species is given by I=4.20.93tspeciesperyear and that the rate of species extinction on the island is given by E=1.51.1tspeciesperyear. According, to the MacArthur-Wilson theory, how long will be required for stabilization to occur, and what will be the immigration and extinction rates at that time?arrow_forward
- Reminder 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. 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 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. Nail Growth The rate of fingernail growth depends on many factors, but in adults, nails grow at an average rate of 3 millimeters per month. If a nail is initially 12 millimeters long, find a formula that gives the length L, in millimeters, of the nail if left unclipped after t months.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Long-Term Population Growth Although exponential growth can often be used to model population growth accurately for some periods of time, there are inevitably, in the long term, limiting factors that make purely exponential models inaccurate. From 1790 to 1860, the U.S. population could be modeled by N=3.931.03tmillion people, where t is the time in years since 1790. If this exponential growth rate had continued until today, what would be the population of the United States have been in 2015? Compare your answer with the actual population of the United States in 2015, which was about 323million.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_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning