PROBLEMS
How Fast Can You List Your Favourite Things? If you are asked to make a list of objects in a certain category, how fast you can list them follows a predictable pattern. For example, if you try to name as many vegetables as you can, you’ll probably think of several right away—for example, carrots, peas, beans, corn and so on. Then after a pause you might think of ones you eat less frequently—perhaps zucchini, eggplant and asparagus. Finally, a few more exotic vegetables might come to mind—artichokes, jicama, bok choy, and the like. A psychologist performs this experiment on a number of subjects. The table below gives the average number of vegetables that the subjects named by a given number of seconds.
(a) Find the cubic polynomial that best fits the data.
(b) Draw a graph of the polynomial from part(a) together with a
(c) Use your result from part(b) to estimate the number of vegetables that subjects would be able to name in 40 s
(d) According to the model, how long (to the nearest 0.1 s) would it take for the person to name five vegetables?
Seconds | Number of vegetables |
1 | 2 |
2 | 6 |
5 | 10 |
10 | 12 |
15 | 14 |
20 | 15 |
25 | 18 |
30 | 21 |
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Algebra and Trigonometry
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