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The monthly charge for a waste collection service is $1035 for 100 kg of waste and $1685 for 165 kg of waste.

(a) Find a linear model for the cost, \( C \), of waste collection as a function of the number of kilograms, \( k \).

Answer :

To find a linear model for the cost of waste collection, use the formula for the equation of a line and two given points. Substitute the values into the formula to calculate the slope and y-intercept. The linear model is C = 10t + 35.

To find a linear model for the cost of waste collection as a function of the number of kilograms, we can use the formula for the equation of a line, which is y = mx + b. Here, y represents the cost of waste collection, x represents the number of kilograms, m represents the slope of the line, and b represents the y-intercept.

We are given two points on the line: (100, 1035) and (165, 1685). We can use these points to find the slope, which is the change in y divided by the change in x.

Slope = (1685 - 1035) / (165 - 100) = 650 / 65 = 10

Now that we have the slope, we can substitute one of the points into the equation of a line to find the y-intercept. Using the point (165, 1685), we have:

1685 = 10 * 165 + b

b = 1685 - 1650 = 35

Therefore, the linear model for the cost of waste collection as a function of the number of kilograms is C = 10t + 35, where C represents the cost and t represents the number of kilograms.

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