Chapter 2.7, Problem 18E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume *V* of water remaining in the tank after *t* minutes as

Find the rate at which water is draining from the tank after (a) 5 min, (b) 10 min, (c) 20 min, and (d) 40 min. At what time is the water flowing out the fastest? The slowest? Summarize your findings.

To determine

**To find:** the rate at which water is draining from the tank after

(a) 5 min

(b) 10 min

(c) 20 min

(d) 40 min

Explanation

**1) Formula**:

Chain rule

**2) Given**:

Volume of water remaining

**3) Calculation**:

Volume of water remaining is

Therefore volume of water drained is

Take derivative with respect to time t.

Using difference formula

Using chain rule

(a) Now substitute

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