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, youll...

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Extracted text: 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, youll 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. Number of Seconds vegetables 2 6. 5. 10 10 12 15 14 20 15 25 18 30 21 (a) Find the cubic polynomial that best fits the data. (Let y be the number of vegetables and x be the time in seconds. Round all numerical values to four decimal places.) y = (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. y y 35 35 30 25 30 25 20 20 15 15 10 10 10 20 30 40 10 20 30 35 35 30 30 25 25 20 20 15 15 10 10 5. 10 20 30 40 10 20 30 (c) Use your result from part (b) to estimate the number of vegetables that subjects would be able to name in 37 s. (Round your answer to the nearest whole number.) vegetables (d) According to the model, how long (to the nearest 0.1 s) would it take a person to name five vegetables?