Chapter 2.8, Problem 66E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

When you turn on a hot -water faucet, the temperature *T* of the water depends on how long the water has been running.

(a) Sketch a possible graph of *T* as a function of the time *t* that has elapsed since the faucet was turned on.

(b) Describe how the rate of change of *T* with respect to *t* varies as *t* increases.

(c) Sketch a graph of the derivative of *T*

(a)

To determine

**To sketch:** The possible graph of *T* as a function of time *t* that has elapsed since the faucet was turned on.

Explanation

**Fact:**

Since temperature *T* is proportional to the time *t* up to which the faucet has been running.

That is, *k* and *c* are constants.

Since at the starting the process the water is present in the pipes whose temperature is same as the room temperature which implies the initial temperature of water in the faucet is nearly equal to the room temperature

(b)

To determine

**To describe:** The rate of change of *T* with respect to the time *t* varies as *t* increases.

(c)

To determine

**To sketch:** The graph of *t* graph.

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