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In a Washington town, the charge for commerical waste collection is $694.55 for 5 tons of waste and $1098.56 for 8 tons of waste. (a) Find a linear formula for the cost, C. of waste collection as a function of the weight, w, in tons.

Answer :

Answer:

[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]

And we can find the intercept like this:

[tex] 694.55 = 134.67*5 +b[/tex]

[tex] b = 694.55 -673.35= 21.2[/tex]

And the equation would be given by:

[tex] C = 134.67 w + 21.2[/tex]

Step-by-step explanation:

For this case we want a function given by:

[tex] C = mw +b[/tex]

Where C is the cost, m the slope, w the weight and b the intercept.

We have the following info (w=5, C= 694.55) and (w=8, C=1098.56) and we can find the slope with this formula:

[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]

And we can find the intercept like this:

[tex] 694.55 = 134.67*5 +b[/tex]

[tex] b = 694.55 -673.35= 21.2[/tex]

And the equation would be given by:

[tex] C = 134.67 w + 21.2[/tex]

MrRoyal

A linear function is a function that changes at a constant rate.

The formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]

The given parameters are:

  • w = 5, C = 694.55 ---- Charges for 5 tons
  • w = 8, C = 1098.56 ---- Charges for 8 tons

Start by calculating the slope (m)

[tex]m = \frac{C_2 - C_1}{w_2 - w_1}[/tex]

This gives

[tex]m = \frac{1098.56 - 694.55 }{8- 5}[/tex]

Simplify

[tex]m = \frac{404.01}{3}[/tex]

This gives

[tex]m = 134.67[/tex]

The equation is then calculated as:

[tex]C = m(w -w_1) + w_1[/tex]

This gives

[tex]C = 134.67(w -5) + 694.55[/tex]

Expand

[tex]C = 134.67w -673.35 + 694.55[/tex]

[tex]C = 134.67w + 21.2[/tex]

Hence, the formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]

Read more about linear equations at:

https://brainly.com/question/14323743

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