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Problem 61

Modeling Data For a long-distance phone call, a hotel charges $\$ 9.99$ for the first minute and $\$ 0.79$ for each additional minute or fraction thereof. A formula for the cost is given by

$C(t)=9.99-0.79[1-t], \quad t>0$

where $t$ is the time in minutes.

(Note: $[x]=$ greatest integer $n$ such that $n \leq x .$ For example,

$[3.2]=3$ and $\mathbb{I}-1.6 \mathbb{l}=-2 . )$

(a) Evaluate $C(10.75) .$ What does $C(10.75)$ represent?

(b) Use a graphing utility to graph the cost function for

$0<t \leq 6 .$ Does the limit of $C(t)$ as $t$ approaches 3 exist? Explain.

Answer

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## Discussion

## Video Transcript

were given a fallen function. C. A. T is equal to 9.99 minus their points overnight. Two brackets of one minus state where those brackets represented nearest and pitcher and see if t represents it. Cost of a long distance phone call and teeth is the not of minutes. So for part, A were asked to analyse See of 10.75 so we can pluck into equation zero point Southern nine one minus 10.75 which is equal to 9.99 minus 0.7 Fine, uh, negative 9.75 And we know that that those brackets just mean to the nearest integer. So we end up with 9.99 minus zero point Southern. I'd of negative ton coast on your son. Sure, they don't quite have five side of time. If we simply simplify all that down, you get 17.89 And so this shows that it costs $17.89 after 10.75 minutes. Art. So for part B were asked, Ask the limit as CFT. So the longer it has a Z t a purchase 30 c ity your ass. Determine if that exists. So to do this, we need to graph it from t it from zero to sex. Been. So looking at this, we can see the other three. Right, Cassie at three. Right here from here to here there. It's not continuous. And so therefore, we know that the limit does not exist, so limit there's not exist.

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