Concept explainers
IQ Scores The IQ scores for a sample of students at a small college roughly follow the
where
(a) Use a graphing utility to graph the function.
(b) From the graph in part (a), estimate the average IQ score of a student.
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Chapter 5 Solutions
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- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forwardDVD Player sales The table shows the number of DVD play-ers sold in a small electronics store in the years 2003-2013. What was the average rate of change of sales between 2003 and 2013? Whatwas the average rate of change of sales between 2003 and 2004? What was the average rate of change of sales between 2004 and 2005? Between which two successive years did DVD player sales increase most quickly?arrow_forwardLet f(x)=1x . Find a number c such that the average rate of change of the functionfon the interval (1,c) is 14arrow_forward
- In Example 7, find the average speed of the car (a) from t1=0tot2=1 second and (b) from t1=1 second to t2=4 seconds.arrow_forwardThe US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?arrow_forwardDVD Player Sales The table shows the number of DVD players sold in a small electronics store in the years 2003-2013. Year DVD players sold 2003 495 2004 513 2005 410 2006 402 2007 520 2008 580 2009 631 2010 719 2011 624 2012 582 2013 635 aWhat was the average rate of change of sales between 2003 and 2013? bWhat was the average rate of change of sales between 2003 and 2004? cWhat was the average rate of change of sales between 2004 and 2005? dBetween which two successive years did DVD player sales increase most quickly? Decrease most quickly?arrow_forward
- What is the visual representation of the average rate of change f(x) = x 2 from x = 1 to x = 3 _____________ ?arrow_forwardIs the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on th depth (in kilometers) of the quake below the surface at the epicenter. y 5.5 10.4 10.0 7.9 (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. Cloudy y (depth (in kilometers)) O (depth (in kilometers)) 10 9 7 4.5 4.0 3.5 3.0 3.5 TE EE x (magnitude of an earthquake (on the Richter scale)) #8 FEE BEEEL BER 4.5 Q Search H 3.4 DO y (depth (in kilometers)) (depth (in kilometers)) 11 10 8 7 6 40 4.5 3.5 FE 3.0 M @ 32 3.5 x (magnitude of an earthquake (on the Richter scale)) hp 89 99+ 4.0 12arrow_forwardt (min) 5 10 15 L(t) (people per min) 150 110 40 20 2. On a certain day, 2000 students were present at Southside High School. At the end of this school day, when the bell rang at 3:00 PM, students left Southside High School the school at a rate of L(t), where t is the number of minutes since the bell rang. Selected values of L(t) are shown in the table above. Using a left Riemann sum with subintervals as indicated in the table, approximate the number of students still inside Southside High School in the 15 minutes after the bell rang. (A) 400 (B) 500 (C) 1150 (D) 1700arrow_forward
- What eventually happens to the concentration of the injection in the blood stream? Explain. Use the graph to explain mathematically and in context. BIarrow_forwardThe graph shows the speed, S (kilometres per hour) of a car as it travels along a straight road at time t hours. speed (km/h) 90 60 30 0.10e 0.20 0.30 0.40e 0.50 0.60e time (h)e What is the maximum speed of the car?e a b During which intervals was the rate of change of the speed of the car zero?e Use the graph to estimate the average rate at which the car's speed is increasing between times 1 = 0.05 hour and t= 0.20 hour.“ d. Find an estimate for the rate at which the car's speed is increasing when 1 = 0.1 hour.“ e When was the speed increasing most rapidly? How can you tell?e Sketch the graph of the rate of change of speed against time for t = 0 to t = 0.50 hour. (General shape and key t values required only on graph; there is no need for a vertical scale.) earrow_forwardUtility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function.arrow_forward
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