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Problem 1 Medium Difficulty

A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume $V$ of water remaining in the tank (in gallons) after $t$ minutes.
$$
\begin{array}{|c|c|c|c|c|c|c|}
\hline t(\mathrm{~min}) & 5 & 10 & 15 & 20 & 25 & 30 \\
\hline V(\mathrm{gal}) & 694 & 444 & 250 & 111 & 28 & 0 \\
\hline
\end{array}
$$
(a) If $P$ is the point (15,250) on the graph of $V$, find the slopes of the secant lines $P Q$ when $Q$ is the point on the graph with $t=5,10,20,25,$ and 30
(b) Estimate the slope of the tangent line at $P$ by averaging the slopes of two secant lines.
(c) Use a graph of the function to estimate the slope of the tangent line at $P$. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)


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Calculus 1 / AB

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