Question

The monthly charge for a waste collection service is 1830 dollars for 100 kg of waste and 2460 dollars for 135 kg of waste. (a) Find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.

Answer 1

`C=18w+30`

Explanation:

We are given that The monthly charge for a waste collection service is 1830 dollars for 100 kg of waste

So,
`(x_1,y_1)=(100,1830)`

We are also given that The monthly charge for a waste collection service is 2460 dollars for 135 kg of waste.

So,
`(x_2,y_2)=(135,2460)`

We are supposed to find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.

So, we will use two point slope form :

Formula :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values

`y-1830=(2460-1830)/(135-100)(x-100)`

`y-1830=18(x-100)`

`y-1830=18x-1800`

`y=18x-1800+1830`

`y=18x+30`

y denotes the cost

x denotes the weight

So, Replace y with C and x with w

`C=18w+30`

So, a linear model for the cost, C, of waste collection as a function of the number of kilograms, w is
`C=18w+30`