Question

A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-

defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
C(x).
18
for (Choose one) Y
for (Choose one) ▼
X
!!

Answer 1

The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

`C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.`

Your system might not require the "0≤x", but it technically should be there.