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The cost, [tex]c(x)[/tex], for a taxi ride is given by [tex]c(x)=2x+4.00[/tex], where [tex]x[/tex] is the number of minutes. What does the slope mean for this situation?

A. The rate of change of the cost of the taxi ride is [tex]\[tex]$2.00[/tex] per minute.
B. The taxi ride costs [tex]\$[/tex]2.00[/tex] per trip.
C. The taxi ride costs a total of [tex]\[tex]$4.00[/tex].
D. The rate of change of the cost of the taxi ride is [tex]\$[/tex]4.00[/tex] per minute.

Sagot :

GinnyAnswer
To understand what the slope means in the context of the cost function for the taxi ride, we need to analyze the function [tex]\( c(x) = 2x + 4.00 \)[/tex].

1. Identify the components of the function:
- [tex]\( c(x) \)[/tex]: This represents the total cost of the taxi ride.
- [tex]\( x \)[/tex]: This represents the number of minutes.
- [tex]\( 2x \)[/tex]: This term represents a cost that varies with the number of minutes [tex]\( x \)[/tex].
- [tex]\( 4.00 \)[/tex]: This is a constant term which represents a fixed base cost regardless of the duration of the ride.

2. Slope of the function:
The function [tex]\( c(x) = 2x + 4.00 \)[/tex] is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In this case, [tex]\( m = 2 \)[/tex].

3. Interpretation of the slope [tex]\( m = 2 \)[/tex]:
- The slope, [tex]\( m = 2 \)[/tex], indicates the rate at which the cost changes for each additional minute of the ride.
- Specifically, for each minute increase in the duration of the taxi ride, the cost increases by \[tex]$2.00. 4. Consider the given options: - Option A: The rate of change of the cost of the taxi ride is \$[/tex]2.00 per minute.
- This option correctly describes the slope of the cost function.
- Option B: The taxi ride costs \[tex]$2.00 per trip. - This option incorrectly describes the slope as a total cost per trip, which is not represented by the slope. - Option C: The taxi ride costs a total of \$[/tex]4.00.
- This option only describes the y-intercept (initial base cost) of the function, not the slope.
- Option D: The rate of change of the cost of the taxi ride is \[tex]$4.00 per minute. - This option incorrectly states the rate of change, which should be \$[/tex]2.00 per minute, not \[tex]$4.00. 5. Conclusion: The correct interpretation of the slope in this context is that the rate of change of the cost of the taxi ride is \$[/tex]2.00 per minute.

Therefore, the correct answer is:

A. The rate of change of the cost of the taxi ride is \$2.00 per minute.
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