3. How Fast Can You List Your Favorite 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 ex- otic vegetables might come to mind-artichokes, jicama, bok choy, and the like. A psycholo- gist 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 scatter plot of the data. (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 a person to name five vegetables?

3. How Fast Can You List Your Favorite 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 ex- otic vegetables might come to mind-artichokes, jicama, bok choy, and the like. A psycholo- gist 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 scatter plot of the data. (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 a person to name five vegetables?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3. How Fast Can You List Your Favorite 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 ex-
otic vegetables might come to mind-artichokes, jicama, bok choy, and the like. A psycholo-
gist 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 scatter plot of the data.
(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 a person to name
five vegetables?
Number of
Seconds
vegetables
2
5
10
10
12
15
14
20
15
25
18
30
21

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