To solve this problem, we need to identify the descriptions and sets of values in both the domain and range of the function [tex]\(W = 7F + 5000\)[/tex].
### Identifying the Domain
1. Description of Values in the Domain:
- The function [tex]\(W = 7F + 5000\)[/tex] expresses [tex]\(W\)[/tex] (the weight of the airplane) as a function of [tex]\(F\)[/tex] (the amount of fuel in the airplane's tank).
- Therefore, the independent variable here is [tex]\(F\)[/tex], which represents the "amount of fuel in airplane's tank (in gallons)."
2. Set of Values in the Domain:
- Since the fuel tank can hold up to 300 gallons, [tex]\(F\)[/tex] can range from 0 gallons (when the tank is empty) to 300 gallons (when the tank is full).
- Hence, the domain of [tex]\(F\)[/tex] is "the set of all real numbers from 0 to 300."
### Identifying the Range
1. Description of Values in the Range:
- The dependent variable is [tex]\(W\)[/tex], which represents the "weight of the airplane (in pounds)."
2. Set of Values in the Range:
- To determine the range, we calculate the minimum and maximum values of [tex]\(W\)[/tex] based on the domain of [tex]\(F\)[/tex].
- When [tex]\(F = 0\)[/tex]:
[tex]\[
W = 7 \cdot 0 + 5000 = 5000 \text{ pounds}
\][/tex]
- When [tex]\(F = 300\)[/tex]:
[tex]\[
W = 7 \cdot 300 + 5000 = 2100 + 5000 = 7100 \text{ pounds}
\][/tex]
- Therefore, the range of [tex]\(W\)[/tex] is "the set of all real numbers from 5000 to 7100."
### Final Answer
Combining our findings, we get the following table:
[tex]\[
\begin{array}{|c|c|c|}
\hline & \text{Description of Values} & \text{Set of Values} \\
\hline \text{Domain:} & \text{amount of fuel in airplane's tank (in gallons)} & \text{the set of all real numbers from 0 to 300} \\
\hline \text{Range:} & \text{weight of airplane (in pounds)} & \text{the set of all real numbers from 5000 to 7100} \\
\hline
\end{array}
\][/tex]
This table accurately represents the domain and range of the function [tex]\(W = 7F + 5000\)[/tex], along with the appropriate descriptions and sets of values.
