Answer :
The linear model for the cost, C, of waste collection as a function of weight, w, is C = 16w + 50.
To find a linear model for the cost of waste collection, we need to determine the equation of a line that represents the relationship between the weight of waste and the corresponding cost.
Let's use the given data points: (100, 1650) and (165, 2690).
We can calculate the slope of the line using the formula:
slope = (change in y) / (change in x) = (2690 - 1650) / (165 - 100) = 1040 / 65 = 16
The slope represents the rate of change of cost with respect to the weight of waste.
Next, we need to find the y-intercept of the line. We can use the point-slope form of a line to calculate it.
Using the point (100, 1650) and the slope m = 16, we have:
1650 = 16(100) + b
Solving for b, the y-intercept, we get:
1650 = 1600 + b
b = 1650 - 1600
b = 50
Now we have the slope (m = 16) and the y-intercept (b = 50). We can write the equation of the line in slope-intercept form as:
C = 16w + 50
Therefore, the linear model for the cost, C, of waste collection as a function of weight, w, is C = 16w + 50.
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