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Answer:
y=4.8710 is the missing value
Step-by-step explanation:
The first step in approaching this question is determining the exponential equation that models the set of data. This can easily be done in Ms.Excel application. We first enter the data into any two adjacent columns of an excel workbook. The next step is to highlight the data, click on the insert tab and select the x,y scatter-plot feature. This creates a scatter-plot for the data.
The next step is to click the Add chart element feature and insert an exponential trend line to the scatter plot ensuring the display equation on chart is checked.
The exponential regression equation for the data set is given as;
To find the missing y value, we simply substitute x with 2 in the regression equation obtained;
When y=0,
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![\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%20%7B%202x%20%7D%5E%7B%202%2B1%20%7D%20%7D%7B%202%2B1%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%201%2B1%20%7D%20%7D%7B%201%2B1%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
![\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%202%7B%20x%20%7D%5E%7B%203%20%7D%20%7D%7B%203%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%202%20%7D%20%7D%7B%202%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
Answer: 343/24 units squared.
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Answer: 343/24 units squared.