Question

fantastic photo offers the following prices for their dog grooming business based on the dogs wait. dogs 10 lbs or less are charged $20 dogs between 10 and 40 lb are charged $35 dogs over 40 pounds are charged $50 plus $2 a pound over 40 pounds which piecewise function represents the cost of dog grooming?

Answer 1

Let the weight of the dogs be w

Let the cost of the dogs as a function of the weight be represented as C(w)

Dogs 10 lbs or less are charged $20

That is, when w ≤ 10, C(w) = 20

Dogs between 10 and 40 lb are charged $35

That is when 10 < w < 40, C(w) = 35

Dogs over 40 pounds are charged $50 plus $2 a pound over 40 pounds

That is, when w > 40, C(w) = 50

When w = 40, C(w) = 2w = 2(40) = 80

The piecewise function can therefore be represented as:

`\begin{gathered} C(w)=\begin{cases}20\text{ if w }\le10\text{ } \\ 35\text{ if 10 < w < 40} \\ 50\text{ if w }>\text{ 40} \\ \text{80 if w = 40}\end{cases} \\ \end{gathered}`

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