Exercise 2.2.1. PROTEUS EXERCISE.
The time (\(T\text{,}\) measured in hours) it takes to drive 50 miles along State Highway 46 depends on the constant speed at which you are driving (\(s\text{,}\) measured in mph). Since
\begin{equation*}
\text{distance traveled} = \text{speed}\cdot \text{travel time},
\end{equation*}
\(T(s) = 50/s.\)
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Draw a graph of this function and explain why the shape of this graph makes sense.
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What is the value of \(T(60)\text{?}\) Give units on your answer. What does this value mean in context?
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Find the average rate of change of \(T\) on the interval \([60, 65]\text{,}\) \(AV_{[60, 65]}\text{.}\) Give units on your answer.
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Is the sign of \(AV_{[60, 65]}\) positive or negative? Why does this sign make sense in light of the graph of \(T(s)\text{?}\) Explain your thinking.
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Write a sentence in everyday language explaining the meaning of the value \(AV_{[60, 65]}\) in context. Include units in your sentence.