Linear models can be used to predict buying habits of consumers. Suppose that a survey found that in 2008,18% of the consumers surveyed in a group bought designer frames for their eyeglasses. In 2011, the percentageclimbed to 24 %a. Assume the percentage of people buying frames is a linear function of time, and find an equation for thepercentage of people buying designer frames. Let t correspond to the number of years since 2008P(t)b. Use your equation to predict the percentage of people buying designer frames in 2014The model predicts the percentage of people buying designer frames in 2014 will be |c. Use your equation to predict when the percentage of people who buy designer frames will reach 50 %The model predicts in the year1, 50% of people will buy designer framesd. Do you think you can use this model to predict the percentage of people buying designer frames in the year2051? Why or why not?

Question
Asked Sep 19, 2019
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Linear models can be used to predict buying habits of consumers. Suppose that a survey found that in 2008,
18% of the consumers surveyed in a group bought designer frames for their eyeglasses. In 2011, the percentage
climbed to 24 %
a. Assume the percentage of people buying frames is a linear function of time, and find an equation for the
percentage of people buying designer frames. Let t correspond to the number of years since 2008
P(t)
b. Use your equation to predict the percentage of people buying designer frames in 2014
The model predicts the percentage of people buying designer frames in 2014 will be |
c. Use your equation to predict when the percentage of people who buy designer frames will reach 50 %
The model predicts in the year
1, 50% of people will buy designer frames
d. Do you think you can use this model to predict the percentage of people buying designer frames in the year
2051? Why or why not?
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Linear models can be used to predict buying habits of consumers. Suppose that a survey found that in 2008, 18% of the consumers surveyed in a group bought designer frames for their eyeglasses. In 2011, the percentage climbed to 24 % a. Assume the percentage of people buying frames is a linear function of time, and find an equation for the percentage of people buying designer frames. Let t correspond to the number of years since 2008 P(t) b. Use your equation to predict the percentage of people buying designer frames in 2014 The model predicts the percentage of people buying designer frames in 2014 will be | c. Use your equation to predict when the percentage of people who buy designer frames will reach 50 % The model predicts in the year 1, 50% of people will buy designer frames d. Do you think you can use this model to predict the percentage of people buying designer frames in the year 2051? Why or why not?

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Expert Answer

Step 1

To set up linear equation(s) corresponding to the given data

Step 2

In this problem, the independent variable is t= the number of years after 2008, and the dependent variable is the percentage P(t). A linear model connecting these two variables will have an equation of the form P(t) = At + B, for some constants to be determined

Step 3
(a)P(t) At+B
2008t=0, P(0) 18= B = 18
2011-3, P(3) 3.4+18 =24 = A = 2
So,the line ar model is P(f)= 2t +18
help_outline

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(a)P(t) At+B 2008t=0, P(0) 18= B = 18 2011-3, P(3) 3.4+18 =24 = A = 2 So,the line ar model is P(f)= 2t +18

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