Final answer:
The question is about creating a table of values and a graph for a cost function, C = 25x + 30, where C is the total cost and x is the number of hours of labor. Values are calculated for x from 0 to 4 hours, and the resulting points can be graphed on a coordinate plane, with the y-intercept (0, 30) and a slope of 25.
Step-by-step explanation:
The student is asking how to use Elaine's business model, where she charges a base fee of $30 and $25 per hour for her labor, to create a table of values and a graph. The cost function for Elaine's services can be expressed as C = 25x + 30, where C represents the total cost for the service and x represents the hours of labor. At zero hours, the cost is simply the base fee of $30. As the number of hours increases, the total cost increases by $25 per hour.
To create a table of values, we select a range of x values (hours of labor), and calculate the corresponding C values (total cost). Here is an example for the first four hours:
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- 0 hours: C = 25(0) + 30 = $30
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- 1 hour: C = 25(1) + 30 = $55
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- 2 hours: C = 25(2) + 30 = $80
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- 3 hours: C = 25(3) + 30 = $105
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- 4 hours: C = 25(4) + 30 = $130
To graph this function, we would plot these pairs of values on a coordinate plane with x on the horizontal axis and C on the vertical axis. The y-intercept is the point (0, 30) and the slope of the line is 25, indicating that for every additional hour of labor, the cost increases by $25.