For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. When necessary, round values to five decimal places: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ \hline f(x) & 20 & 21.6 & 29.2 & 36.4 & 46.6 & 55.7 & 72.6 & 87.1 & 107.2 & 138.1

ruigE 2021-08-01 Answered

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
\(\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline f(x) & 20 & 21.6 & 29.2 & 36.4 & 46.6 & 55.7 & 72.6 & 87.1 & 107.2 & 138.1 \\ \hline \end{array}\)

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Expert Answer

Mitchel Aguirre
Answered 2021-08-02 Author has 17525 answers

Step 1
Remember that regression analysis is the process of looking for a best fit of model for a set of data. This can be done on a graphing utility as follows:
1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
2. Use [STATPLOT] to observe a scatterplot of the data.
3. Press [STAT], then [CALC] then [ExpReg]/[LnReg]/[Logistic].
This will show you a function in either the form of an exponential, a logarithmic or a logistic model.
4. Graph this equation on the same window as the scatterplot to see if it fits the data.
Step 2
1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
2. Use [STATPLOT] to observe a scatterplot of the data.
image

Step 3
Based on the plots of the points, it can be exponential or logarithmic.
However, upon checking both regression analysis, the one with the closest value of \(\displaystyle{r}^{{{2}}}\) to 1 is exponential, hence, its formula is \(\displaystyle{y}={15.10062}{\left({1.24621}\right)}^{{{x}}}\). The graph of which is below:
image Answer:\(\displaystyle{y}={15.10062}{\left({1.24621}\right)}^{{{x}}}\)
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asked 2021-08-08

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
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asked 2021-08-06

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Use exponential regression to find a function that models the data. \(\begin{array}{|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 \\ \hline \end{array}\)

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The popularity of fads and fashions often decays exponentially. One example is ticket sales for a popular movie. The table shows the total money spent per weekend on tickets in the United States and Canada for the movie The Da Vinci Code.
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a) Use a graphing calculator to create a scatter plot of the data.

b) Draw a quadratic curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 5:QuadReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 1:Y1. - Press ENTER to get the QuadReg screen, and press GRAPH.

c) Draw an exponential curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 0:ExpReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 2:Y2. - Press ENTER to get the ExpReg screen, and press GRAPH.

d) Examine the two curves. Which curve of best fit best models the data?

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