Answer :
To find the function that best models the data, we can determine the equation of the line that best fits the given data points using a linear function. The data points are:
- Months ([tex]$x$[/tex]): 0, 1, 2, 3, 4, 5
- Percentage left to build ([tex]$y$[/tex]): 100, 86, 65, 59, 41, 34
The goal is to check each provided linear function to see which one best matches the pattern of this data.
Let's verify the options:
1. [tex]$y = -135x + 97.8$[/tex]
2. [tex]$y = -13.5x + 7.3$[/tex]
3. [tex]$y = 97.8x - 135$[/tex]
4. [tex]$y = 7.3x - 97.8$[/tex]
Through analysis, we determine the following:
1. Slope and Intercept:
- Calculating the slope and intercept through a fitting process, we find:
- Slope (rate of change): Approximately -13.46
- Intercept (initial value when [tex]$x=0$[/tex]): Approximately 97.81
2. Matching with Functions:
- Option 1: The slope (-135) and intercept (97.8) clearly do not match our findings.
- Option 2: The slope (-13.5) is close to -13.46, but the intercept (7.3) is far from 97.81.
- Option 3: The slope (97.8) and intercept (-135) do not match our determined values.
- Option 4: The slope (7.3) and intercept (-97.8) do not match our findings.
Based on our findings, none of the options perfectly matches the calculated slope and intercept values from the data. If we round the slope to -13.5 and the intercept to 97.8, Option 2 might appear close in its slope value but is incorrect for the intercept.
Thus, none of the provided functions exactly model the calculated slope and intercept from the data.
- Months ([tex]$x$[/tex]): 0, 1, 2, 3, 4, 5
- Percentage left to build ([tex]$y$[/tex]): 100, 86, 65, 59, 41, 34
The goal is to check each provided linear function to see which one best matches the pattern of this data.
Let's verify the options:
1. [tex]$y = -135x + 97.8$[/tex]
2. [tex]$y = -13.5x + 7.3$[/tex]
3. [tex]$y = 97.8x - 135$[/tex]
4. [tex]$y = 7.3x - 97.8$[/tex]
Through analysis, we determine the following:
1. Slope and Intercept:
- Calculating the slope and intercept through a fitting process, we find:
- Slope (rate of change): Approximately -13.46
- Intercept (initial value when [tex]$x=0$[/tex]): Approximately 97.81
2. Matching with Functions:
- Option 1: The slope (-135) and intercept (97.8) clearly do not match our findings.
- Option 2: The slope (-13.5) is close to -13.46, but the intercept (7.3) is far from 97.81.
- Option 3: The slope (97.8) and intercept (-135) do not match our determined values.
- Option 4: The slope (7.3) and intercept (-97.8) do not match our findings.
Based on our findings, none of the options perfectly matches the calculated slope and intercept values from the data. If we round the slope to -13.5 and the intercept to 97.8, Option 2 might appear close in its slope value but is incorrect for the intercept.
Thus, none of the provided functions exactly model the calculated slope and intercept from the data.
