Question

Math IIIB Performance Task: Piecewise-Defined Functions

Answer 1

9514 1404 393

Explanation:

a) see the attachment for a graph (red curve)

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b) The piecewise defined function can be ...

  $\displaystyle C(x)=\begin{cases}0&0\le x\le 1\\5&1$

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c) The new cost function is ...

  $\displaystyle C(x)=\begin{cases}10&0\le x\le5\\x+5&5$

The charge is a flat $10 for any period up to 5 hours, then $1 per additional hour after that, prorated for partial hours. There is apparently no upper limit on parking time as there was with the original function. (The graph shown goes beyond 15 hours; the domain of the original C(x) is 0 to 12 hours.) For reference, the new cost structure is shown in blue in the attachment.

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Additional comment

Under the new structure, costs are significantly higher for short-term parking, and lower once the term exceeds 6 hours.