Chapter 5.1, Problem 35E

How are the absolute maximum and minimum similar to and different from the local extrema?

Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa. x 2 3 5 8 10 y 2 3 12 125 630   (a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good fit to these data? Do the y values almost seem to explode as time goes on? No. A straight line does not fit the data well. The data seem to explode as x increases.Yes. A straight line does not fit the data well. The data seem to explode as x increases.     No. A straight line does not fit the data well. The data does not seem to explode as x increases.Yes. A straight line seems to fit the data well. The data seem to explode as x increases. (b) Now consider a transformation y' = log (y). We are using common logarithms of base 10. Draw a scatter diagram of the (x, y') data pairs and compare this diagram with the diagram of part (a). Which graph appears to better fit a straight line? The two diagrams are the same. The…

Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is ŷ =−0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables Video Games(minutes) Time with Family(minutes) 30 50 60 40 90 35 120 25   According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction? Select the correct answer below: The estimate, a predicted time of  31.85 minutes, is unreliable but reasonable. The estimate, a predicted time of  31.85 minutes, is both unreliable and unreasonable. The estimate, a predicted time of  31.85 minutes, is both reliable and reasonable. The estimate, a predicted time of  31.85 minutes, is reliable but unreasonable.