Answer :
To find the weight of the cheetah and determine whether interpolation or extrapolation is used, let's go through the process step by step.
1. Understand the Problem: We are given a linear equation that models the weight of a cheetah based on the number of miles it runs per day:
[tex]\[
y = 195 - 7.3x
\][/tex]
Here, [tex]\( y \)[/tex] represents the weight of the cheetah in pounds, and [tex]\( x \)[/tex] represents the miles run.
2. Input the Value: The problem provides that the cheetah runs 10 miles a day, which means [tex]\( x = 10 \)[/tex].
3. Calculate the Weight: Substitute [tex]\( x = 10 \)[/tex] into the equation to find the weight [tex]\( y \)[/tex].
[tex]\[
y = 195 - 7.3 \times 10
\][/tex]
[tex]\[
y = 195 - 73
\][/tex]
[tex]\[
y = 122
\][/tex]
So, the weight of the cheetah is 122 pounds.
4. Determine Interpolation or Extrapolation:
- Interpolation involves estimating a value within the range of known data points.
- Extrapolation involves estimating a value outside the range of known data points.
The scenario suggests that the cheetah's weight for running 10 miles per day results in extrapolation, based on the context or additional information provided, implying that 10 miles is outside the scope of typical data used in the scatter plot analysis originally related to this linear equation.
Therefore, the solution indicates that the weight of the cheetah is 122 pounds, and this involves extrapolation.
1. Understand the Problem: We are given a linear equation that models the weight of a cheetah based on the number of miles it runs per day:
[tex]\[
y = 195 - 7.3x
\][/tex]
Here, [tex]\( y \)[/tex] represents the weight of the cheetah in pounds, and [tex]\( x \)[/tex] represents the miles run.
2. Input the Value: The problem provides that the cheetah runs 10 miles a day, which means [tex]\( x = 10 \)[/tex].
3. Calculate the Weight: Substitute [tex]\( x = 10 \)[/tex] into the equation to find the weight [tex]\( y \)[/tex].
[tex]\[
y = 195 - 7.3 \times 10
\][/tex]
[tex]\[
y = 195 - 73
\][/tex]
[tex]\[
y = 122
\][/tex]
So, the weight of the cheetah is 122 pounds.
4. Determine Interpolation or Extrapolation:
- Interpolation involves estimating a value within the range of known data points.
- Extrapolation involves estimating a value outside the range of known data points.
The scenario suggests that the cheetah's weight for running 10 miles per day results in extrapolation, based on the context or additional information provided, implying that 10 miles is outside the scope of typical data used in the scatter plot analysis originally related to this linear equation.
Therefore, the solution indicates that the weight of the cheetah is 122 pounds, and this involves extrapolation.
