A company installs underground cable at a cost of $500 for the first 50 m (or up to 50 m) and$5 for each metre thereafter. Express the cost, C, as a function of the length, l, of undergroundcable. What is the domain of this function?
Question
A company installs underground cable at a cost of 5 for each metre thereafter. Express the cost, C, as a function of the length, l, of undergroundcable. What is the domain of this function?
Solution
The cost function can be expressed in two parts.
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If the length of the cable, l, is less than or equal to 50 m, the cost, C, is a constant $500. This can be written as C(l) = 500 for 0 <= l <= 50.
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If the length of the cable, l, is more than 50 m, the cost, C, is 5 for each additional meter. This can be written as C(l) = 500 + 5(l - 50) for l > 50.
So, the cost function C(l) can be defined as:
C(l) = {500, for 0 <= l <= 50; 500 + 5(l - 50), for l > 50}
The domain of this function is all non-negative real numbers, or [0, ∞), because the length of the cable cannot be negative.
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