For a long distance phone call, a hotel charges $9.99 for the first minute and $0.79 for
Chapter 1, Problem 33(choose chapter or problem)
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
\(C(t)=9.99-0.79 ⟦-(t-1) ⟧\)
where t is the time in minutes.
(Note: \(⟦x⟧\) = greatest integer n such that \(n \leq x\). For example, \(⟦3.2⟧=3\) and \(⟦-1.6⟧=-2\).)
(a) Use a graphing utility to graph the cost function for \(0<t \leq 6\).
(b) Use the graph to complete the table and observe the behavior of the function as t approaches 3.5. Use the graph and the table to find
\(\lim_{t\rightarrow3.5}\ C(t)\)
(c) Use the graph to complete the table and observe the behavior of the function as t approaches 3.
Does the limit of C(t) as t approaches 3 exist? Explain.
Text Transcription:
C(t) = 9.99 - 0.79 left square bracket -(t-1) right square bracket
left square bracket x right square bracket
n leq x
left square bracket 3.2 right square bracket = 3
left square bracket -1.6 right square bracket = -2
0 < t leq 6
lim_t rightarrow 3.5 C(t)
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