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2. A dog breeder's pricing model includes a per puppy charge along with a fired service fee. A litter with
puppies costs $172 and a litter with 10 puppies costs $220 Write an equation that could be used to
calculate the cost. C of taking care or a litter with an member of puppies. p.

Respuesta :

The linear function that models the situation is given by:

[tex]C(p) = 100 + 12p[/tex]

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A linear function for the cost C of taking care of p puppies has the following format:

[tex]C(p) = C(0) + ap[/tex]

In which:

  • C(0) is the fixed cost.
  • a is the slope, which is the cost per puppy.

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  • With 6 puppies, it costs $172. With 10 puppies, it costs $220. The slope is given by the change in the output(cost) divided by the change in the input(number of puppies), thus:

[tex]a = \frac{220 - 172}{10 - 6} = 12[/tex]

Thus:

[tex]C(p) = C(0) + 12p[/tex]

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The cost of $172 with 6 puppies means that when p = 6, C = 172, and we use this to find C(0).

[tex]C(p) = C(0) + 12p[/tex]

[tex]172 = C(0) + 12(6)[/tex]

[tex]C(0) = 172 - 72[/tex]

[tex]C(0) = 100[/tex]

Thus, the linear model is:

[tex]C(p) = 100 + 12p[/tex]

A similar problem is given at https://brainly.com/question/16302622

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