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File Tools View Document5 - Word - X H (C) In Problems 2-5, use the description of the function to sketch a possible graph. Put a label on each axis and state whether the function is increasing or decreasing. 2. The height of a sand dune is a function of time, and the wind erodes away the sand dune over time. 4. The number of air conditioning units sold is a function of temperature, and goes up as the temperature goes up. t (min) b 7. Let W = f(t) represent wheat production in Argentina,4 in millions of metric tons, where t is years since 2010. Interpret the statement f(5) = 49.2 in terms of wheat production. 8. The chirp rate, C, in chirps per minute, of the snowy tree cricket is given by C = f(T) = 4T - 160 where T is degrees Fahrenheit. (a) What does the statement f(30) = 10 mean in terms of temperature? Include units for 30 and for 10 in your answer. (a) Find an appropriate domain of f in the context of the model assuming a maximum temperature of 134"F, the highest recorded (b) Explain what the vertical intercept, a, and the horizontal intercept, b, represent in terms of temperature of the object and at a weather station.5 time outside. (b) Find the range of f on this domain. 30. The gas mileage of a car (in miles per gallon) is highest when the car is going about 45 miles per hour and is lower when the car is going faster or slower than 45 mph. Graph gas mileage as a function of speed of the car. 16. Let y = f(x) = x2 + 2. 34. Figure 1.15 shows fifty years of fertilizer use in the US, India, and the former Soviet Union.10 (a) Find the value of y when x is zero. (b) What is f(3)? A line graph shows years on the horizontal axis from 19 50 to 2000 in 10-year increments and million tons of fertilizer on the vertical axis from 0 to 30 in increments of 5. The line for fertilizer use in the US starts from the 4 on the vertical axis and with (c) What values of x give y a value of 11? a growing trend reaches to a value slightly above 5 by 1960. The line grows further and reaches close to 12 by 1970. The line reaches to a value of 17.5 by 1980 and remains almost unchanged thereafter. The line for Former Soviet Union almost overlaps (d) Are there any values of x that give y a value of 1? the line for India until 1960 where it shows a sudden growth to reach to a value close to 8 by 1970. The line reaches to a peak " In Problems 17-20 the function S = f(t) gives the average annual sea level, S, in meters, in Aberdeen, Scotland,7 as a function value of 27 by 1985 where it shows a sudden decline to fall down to a value of close to 5 by 1997. The line falls down further to of t, the number of years before 2012. Write a mathematical expression that represents the given statement. 2.5 by 2000. The values used in the description are approximate. million tons 17. In 2000 the average annual sea level in Aberdeen was 7.049 meters. of fertilizer 18. The average annual sea level in Aberdeen in 2012. 30 Former Soviet Union 25 19. The average annual sea level in Aberdeen was the same in 1949 and 2000. 20 20. The average annual sea level in Aberdeen decreased by 8 millimeters from 2011 to 2012. 15 22. An object is put outside on a cold day at time t = 0 minutes. Its temperature, H = f(t), in 'C, is graphed in Figure 1.8. 10 US 5 India A line graph shows t (minutes) on the horizontal axis and H (degree C) on the vertical axis. The curve in the graph slopes -year downward from point (0, a) and intersects the horizontal axis at point (b, 0). 1950 1960 1970 1980 1990 2000 (a) Estimate fertilizer use in 1970 in the US, India, and the former Soviet Union. (b) Write a sentence for each of the three graphs describing how fertilizer use has changed in each region over this 50-year period. Screens 1-2 of 2 Focus BE 130%