How Do You Calculate the Cost of a Phone Call with a Piecewise Function?

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SUMMARY

The discussion focuses on calculating the cost of a phone call using a piecewise function based on a specific pricing structure. For calls lasting 20 minutes or less, the cost is a flat rate of $0.99. For calls exceeding 20 minutes, the cost is $0.99 for the first 20 minutes, plus $0.07 for each additional minute. The piecewise function can be defined as: C(x) = 0.99 for 0 ≤ x ≤ 20, and C(x) = 0.99 + 0.07(x - 20) for x > 20.

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  • Concept of linear pricing models
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Students in mathematics, telecommunications analysts, and anyone interested in understanding cost calculations using piecewise functions.

Rusho
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A phone company offers a deal by which a long distance phone call costs .99 cents for the first 20 minutes and .07 per minute thereafter. Write a piecewise-defined function for the cost C of making a phone call that lasts x minutes.

So I did this:


f(x) { .99(6) 0<= x
.99(20) 0=> x >= 20

Not a clue what I'm doing...:mad: :mad: :mad:
 
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Okay, say you make a x-minute phone call (x <= 20), i.e a phone call that lasts no longer than 20 minutes. How much will you have to pay if you know that each minute costs you .99 cents?
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If you make a y-minute phone call (y > 20), i.e a phone call that lasts more than 20 minutes. How much will you have to pay for the first 20 minutes? How much will you have to pay for the (y - 20) minutes last? Then do you know how much will you have to pay for that whole y-minute phone call?
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Your function will look like this:
[tex]f(x) := \left\{ \begin{array}{l} ... , \quad \quad \mbox{if } 0 \leq x \leq 20 \\ ... , \quad \quad \mbox{if } x > 20 \end{array} \right.[/tex]
Can you go from here? :)
 

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