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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.

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