To analyze the situation, let's break down the functions given for each city:
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For Houston, the number of paths is modeled by \( y = 4 \). This indicates that the number of paths in Houston is constant (4 paths), regardless of the value of \( x \).
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For Nashville, the number of paths is modeled by \( y = 4x \). This indicates that the number of paths in Nashville increases linearly with \( x \). Specifically, for every increase in \( x \), the number of paths increases by 4.
Now, let's evaluate the given statements:
A. The number of paths planned for Nashville is increasing exponentially.
- This statement is false because the function for Nashville is linear (\( y = 4x \)), not exponential.
B. The number of paths planned for Houston is represented by the green line.
- This cannot be determined as true or false without seeing the graph, but typically a constant function would be a horizontal line.
C. The number of paths planned for Nashville is represented by the green line.
- Similar to B, this cannot be confirmed true or false without seeing the graph.
D. The number of paths planned for Nashville will more than likely exceed the paths in Houston as the value of x increases.
- This statement is true because as \( x \) increases, the number of paths in Nashville (\( 4x \)) will eventually exceed the constant number of paths in Houston (4), specifically when \( x \) is greater than 1.
Given these evaluations, the correct answer is D: The number of paths planned for Nashville will more than likely exceed the paths in Houston as the value of x increases.
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