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The manager of a restaurant found that the cost to produce 200 cups of coffee is ​$20.15​, while the cost to produce 500 cups is ​$548.35. Assume the cost​ C(x) is a linear function of​ x, the number of cups produced. Answer parts a through f.
a. Find a formula for​ C(x).

Respuesta :

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Answer:

C(x)=1.76067x - 331.98

Step-by-step explanation:

We are given two points (x,y) of the linear function C(x):

P1 = (200; 20.15) and P2 = (500; 548.35)

The slope of the function, 'm', can be found by:

[tex]m = \frac{y_1-y_2}{x_1-x_2} \\m = \frac{548.35-20.15}{500-200}\\m= 1.7607[/tex]

Applying point P1 to the general linear equation gives us C(x):

[tex](C-C_1) = m(x-x_1)\\C-20.15=1.76067(x-200)\\C(x)=1.76067x - 331.98[/tex]

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