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# Table 1.40 shows mens and womens world records for swimming distances from 50 meters to

ISBN: 9780470484753 315

## Solution for problem 1.6.12 Chapter 1-6

Functions Modeling Change: A Preparation for Calculus | 4th Edition

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Problem 1.6.12

Table 1.40 shows mens and womens world records for swimming distances from 50 meters to 1500 meters.22 (a) What values would you add to Table 1.40 to represent the time taken by both men and women to swim 0 meters? (b) Plot mens time against distance, with time t in seconds on the vertical axis and distance d in meters on the horizontal axis. It is claimed that a straight line models this behavior well. What is the equation for that line? What does its slope represent? On the same graph, plot womens time against distance and find the equation of the straight line that models this behavior well. Is this line steeper or flatter than the mens line? What does that mean in terms of swimming? What are the values of the vertical intercepts? Do these values have a practical interpretation? (c) On another graph plot the womens times against the mens times, with womens times, w, on the vertical axis and mens times, m, on the horizontal axis. It should look linear. How could you have predicted this linearity from the equations you found in part (b)? What is the slope of this line and how can it be interpreted? A newspaper reporter claims that the womens records are about 8% slower than the mens. Do the facts support this statement? What is the value of the vertical intercept? Does this value have a practical interpretation?

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Table 1.40 shows mens and womens world records for swimming distances from 50 meters to

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