Suppose that a fire truck is parked in front of a building

Chapter 6, Problem 52

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Suppose that a fire truck is parked in front of a building as shown in the figure. FIRE LANE d 10 ft A The beacon light on top of the fire truck is located 10 feet from the wall and has a light on each side. If the beacon light rotates 1 revolution every 2 seconds, then a model for determining the distance d, in feet, that the beacon of light is from point A on the wall after t seconds is given by d1t2 = | 10 tan1pt2| (a) Graph d1t2 = | 10 tan1pt2| for 0 t 2. (b) For what values of t is the function undefined? Explain what this means in terms of the beam of light on the wall. (c) Fill in the following table. (d) Compute d10.12 - d102 0.1 - 0 , d10.22 - d10.12 0.2 - 0.1 , and so on, for each consecutive value of t. These are called first differences. (e) Interpret the first differences found in part (d). What is happening to the speed of the beam of light as d increases?