Section 1.3 Version 1

Transcription

1 Section 1.3 Version 1 1. The following table shows the income tax T owed in a certain state as a function of the taxable income I, both measured in dollars. Make a table showing, for each of the intervals in the tax table below, the average rate of change in T. I = Taxable income T = Tax owed 12, , , , A) Income interval Average rate of change in T From 12,100 to 14, From 14,400 to 15, From 15,500 to 17, B) Income interval Average rate of change in T From 12,100 to 14, From 14,400 to 15, From 15,500 to 17, C) Income interval Average rate of change in T From 12,100 to 14, From 14,400 to 15, From 15,500 to 17, D) Income interval Average rate of change in T From 12,100 to 14, From 14,400 to 15, From 15,500 to 17, E) Income interval Average rate of change in T From 12,100 to 14, From 14,400 to 15, From 15,500 to 17, Version 1 Page 1

2 2. The following table shows the income tax T owed in a certain state as a function of the taxable income I, both measured in dollars. Would you expect T to have a limiting value? Why? I = Taxable income T = Tax owed 12, , , , A) Yes, because the general trend in the average rate of change is not continuously decreasing. B) No, because the average rate of change for 12,300 to 15,800 is not decreasing. C) Yes, because the average rate of change for 14,200 to 15,800 is decreasing. D) No, because the average rate of change does not approach 0 as I decreases. E) Yes, because the average rate of change for 12,300 to 17,900 is decreasing. 3. The Margaria-Kalamen test is used by physical educators as a measure of leg strength. An individual runs up a staircase, and the elapsed time from the third to the ninth step is recorded. The power score is calculated using a formula involving the individual s weight, the height of the stairs, and the running time. The following table shows the power scores required of men for an excellent rating for selected ages. During which 10- year period from age 25 to 55 would you expect to see the greatest decrease in leg power? Age Power score for excellent rating A) 18 to 25 B) 25 to 35 C) 35 to 45 D) 45 to 55 E) 25 to 55 Version 1 Page 2

3 4. The following is the graph of a function f = f ( x). What is the value of f ( 1.2) your answer to one decimal place.. Round A) 2.1 B) 1.7 C) 2.5 D) 2.7 E) 1.9 Version 1 Page 3

4 5. The following is the graph of a function f = f ( x). What is the smallest value of x for which f ( x ) = 2. Round your answer to one decimal place. A) 3.6 B) 1.6 C) 0.8 D) 1.2 E) The following is the graph of the function f(x). Where is the graph increasing? A) from 10 to 0 B) from 1 to 10 C) from 5 to 1 D) from 2 to 10 E) from 5 to 5 Version 1 Page 4

5 7. Sketch the graph of a function f = f (x) if f has a maximum value of 1.33 when x = 0.33, and f has a zero at x = 1. A) B) C) D) Version 1 Page 5

6 E) Version 1 Page 6

7 8. Sketch a graph that is always decreasing but starts out concave up and then changes to concave down. Mark the point of inflection in your graph. A) B) C) D) Version 1 Page 7

8 E) Version 1 Page 8

9 9. A stock market investment of $12,000 was made in During the decade of the 1970s, the stock lost half its value. Beginning in 1980, the value increased until it reached $28,000 in After that its value has remained stable. Let v = v(d) denote the value of the stock, in dollars, as a function of the date d. Make a graph of v against d. A) B) C) D) Version 1 Page 9

10 E) Version 1 Page 10

11 10. The graph below shows the mean flow F for the Arkansas River, in cubic feet of water per second, as a function of the time t, in months, since the start of the year. The flow is measured near the river's headwaters in the Rocky Mountains. Estimate the average rate of change per month in the flow during the first 5 months of the year A) 90 B) 110 C) 480 D) 240 E) 170 Version 1 Page 11

12 11. The graph below shows the temperature T = T(v) 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. At what wind speed is the temperature adjusted for wind chill equal to 5? A) 20 mph B) 11 mph C) 40 mph D) 13 mph E) 5 mph Version 1 Page 12

13 12. The graph below shows the temperature T = T(v) 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. If v changes from 10 mph to 15 mph, what would be the change in the corresponding T(v) values? A) from 8 degrees Fahrenheit to 16 degrees Fahrenheit B) from 3 degrees Fahrenheit to 4 degrees Fahrenheit C) from 7 degrees Fahrenheit to 27 degrees Fahrenheit D) from 2.2 degrees Fahrenheit to 3.8 degrees Fahrenheit E) from 15 degrees Fahrenheit to 8 degrees Fahrenheit Version 1 Page 13

14 13. The graph below shows the number T = T(d) of tornadoes reported by the Oklahoma Climatological Survey. Estimate the average yearly decrease in tornadic activity from 2001 to 2002? A) 88 tornadoes per year B) 66 tornadoes per year C) 42 tornadoes per year D) 57 tornadoes per year E) 76 tornadoes per year 14. The graph below shows the number T = T(d) of tornadoes reported by the Oklahoma Climatological Survey. Estimate the the average yearly rate of change in tornadic activity from 1999 to 2003? A) tornadoes per year B) tornadoes per year C) tornadoes per year D) tornadoes per year E) tornadoes per year Version 1 Page 14

15 15. Suppose the amount of carbon dioxide in the air is influenced by several factors, including respiration of plants. The following figure shows the concentration of carbon dioxide in parts per million (PPM) in a closed (that is, unventilated) greenhouse on a cold, clear day during a 24-hour period beginning at 6 a.m. When is carbon dioxide in the greenhouse at its highest concentration? A) The maximum concentration is attained over the entire interval from about 9 a.m. to about 2 p.m. B) The maximum concentration is attained over the entire interval from about 6 a.m. to about 9 a.m. C) The maximum concentration is attained at about 2 p.m. D) The maximum concentration is attained at about 10 a.m. E) The maximum concentration is attained at about 2 a.m. Version 1 Page 15

16 16. Fertilizer can increase crop production, but the cost of the fertilizer must be taken into account. The following curved graph shows the added bushels per acre of corn that resulted from fertilizer application versus pounds per acre of nitrogen applied. The straight line shows the cost (in bushels of corn, not dollars) versus pounds per acre of nitrogen applied. How many pounds per acre of nitrogen should be applied to achieve maximum profit? A) about 120 pounds of nitrogen per acre should be applied to produce maximum profit B) nitrogen should not be applied to produce maximum profit C) about 70 pounds of nitrogen per acre should be applied to produce maximum profit D) about 40 pounds of nitrogen per acre should be applied to produce maximum profit E) about 100 pounds of nitrogen per acre should be applied to produce maximum profit Version 1 Page 16

17 Answer Key 1. A 2. D 3. C 4. A 5. D 6. A 7. C 8. B 9. E 10. D 11. C 12. E 13. C 14. C 15. B 16. C Version 1 Page 17