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Answer :
The cost of producing solar panels for the company is a linear function of the number of panels produced. To find the cost of producing 5 panels, we can use the given information.
Let's start by finding the slope of the linear function. The slope represents the rate of change in cost per panel. We can calculate the slope using the formula:
Slope = (Cost of producing 12 panels - Cost of producing 2 panels) / (Number of panels for 12 panels - Number of panels for 2 panels)
Slope = ($9400 - $2400) / (12 - 2)
= $700 / 10
= $70
Now that we have the slope, we can find the y-intercept, which represents the fixed cost of production. We can choose any point (x, y) on the line and use the slope to calculate the y-intercept. Let's use the point (2, $2400):
y = mx + b
$2400 = $70 * 2 + b
$2400 = $140 + b
b = $2400 - $140 = $2260
Now we have the equation for the linear function:
Cost = $70 * Number of panels + $2260.
To find the cost of producing 5 panels, we substitute the number of panels with 5 in the equation:
Cost = $70 * 5 + $2260
Cost = $350 + $2260
Cost = $2610
So, the cost of producing 5 panels is $2610.
The cost of producing 5 panels is $2610.
To find the cost of producing 5 panels, we can use the given information and apply the concept of a linear function. A linear function represents a straight line on a graph and can be written in the form y = mx + b, where y is the dependent variable (cost), x is the independent variable (number of panels), m is the slope (rate of change), and b is the y-intercept (fixed cost).
Using the given information, we can calculate the slope by finding the change in cost divided by the change in the number of panels. The slope represents the rate of change in cost per panel. In this case, the slope is $70, indicating that for every additional panel produced, the cost increases by $70.
Next, we can find the y-intercept by substituting the values of a known point (2 panels, $2400 cost) into the linear function equation. By solving for b, we find that the y-intercept is $2260, which represents the fixed cost of production.
With the slope and y-intercept known, we can now form the equation for the linear function: Cost = $70 * Number of panels + $2260. Substituting 5 panels into the equation, we find that the cost of producing 5 panels is $2610.
the cost of producing 5 panels is $2610.
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