The data in the table gives the percentage of MySpace users who are a certain ageUse the data for females.MySpace Users of a Certain Age and Genderas a Percentage of all MySpace UsersFemale, f(percent)MaleAge(years)(percent)179.68.8197.87.6216.16.0235.14.6254.34.0273.84.4292.42.7312.11.9331.21.5351.11.3(a) Align the input data to the number of years x after 17. Find an exponential function that models the MySpace female user data. (Round all numerical values to three decimal places.)f(x)=(b) According to the model in part (a), what is the percentage change in the percentage in your model?%(c) What percentage of female MySpace users are 20 years old? (Round your answer to one decimal place.)%What percentage of female MySpace users are 30 years old? (Round your answer to one decimal place.)%Are these answers found using extrapolation or interpolation?extrapolationinterpolation

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Asked Aug 28, 2019
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The data in the table gives the percentage of MySpace users who are a certain age
Use the data for females.
MySpace Users of a Certain Age and Gender
as a Percentage of all MySpace Users
Female, f
(percent)
Male
Age
(years)
(percent)
17
9.6
8.8
19
7.8
7.6
21
6.1
6.0
23
5.1
4.6
25
4.3
4.0
27
3.8
4.4
29
2.4
2.7
31
2.1
1.9
33
1.2
1.5
35
1.1
1.3
(a) Align the input data to the number of years x after 17. Find an exponential function that models the MySpace female user data. (Round all numerical values to three decimal places.)
f(x)=
(b) According to the model in part (a), what is the percentage change in the percentage in your model?
%
(c) What percentage of female MySpace users are 20 years old? (Round your answer to one decimal place.)
%
What percentage of female MySpace users are 30 years old? (Round your answer to one decimal place.)
%
Are these answers found using extrapolation or interpolation?
extrapolation
interpolation
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The data in the table gives the percentage of MySpace users who are a certain age Use the data for females. MySpace Users of a Certain Age and Gender as a Percentage of all MySpace Users Female, f (percent) Male Age (years) (percent) 17 9.6 8.8 19 7.8 7.6 21 6.1 6.0 23 5.1 4.6 25 4.3 4.0 27 3.8 4.4 29 2.4 2.7 31 2.1 1.9 33 1.2 1.5 35 1.1 1.3 (a) Align the input data to the number of years x after 17. Find an exponential function that models the MySpace female user data. (Round all numerical values to three decimal places.) f(x)= (b) According to the model in part (a), what is the percentage change in the percentage in your model? % (c) What percentage of female MySpace users are 20 years old? (Round your answer to one decimal place.) % What percentage of female MySpace users are 30 years old? (Round your answer to one decimal place.) % Are these answers found using extrapolation or interpolation? extrapolation interpolation

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Expert Answer

Step 1

As a first step we need to set the input data to the number of years x after 17. Please see the table on the white board.

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Age (years) Female, f (%) A 17 A 9.60% 17.00 7.80% 19.00 2.00 6.10% 21.00 4.00 6.00 5.10% 23.00 4.30% 25.00 8.00 3.80% 27.00 10.00 2.40% 29.00 12.00 2.10% 31.00 14.00 1.20% 1.10% 33.00 16.00 35.00 18.00

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Step 2

W enow need to plot the given data and find the corresponding exponential function, fitting the data well. We will achieve this step by adding a trendline and selecting the exponential functon. Please see the white board.

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E G H K Female, f (%) 12.00% 10.00% 8.00% Series "Female, Fill Outline 6.00% Delete 4.00% Reset to Match Style Change Series Chart Type... 2.00% Select Data... O3-D Rotation.. 0.00% Add Data Labels 2.00 4.00 12.00 14.00 16.00 18.00 Add Trendline... Eormat Data Series...

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Step 3

Part (a)

We will get the trendline as shown on the white board.

Recall the formula: exln(a) = ax

In our case, ln(a) = -0.244

Hence, a  ...

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Female, f (%) 12.00% 10.00% 8.00% 6.00% y=0.133e-0.244x R2 0.9758 4.00% 2.00% 0.00% 4.00 2.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

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