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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

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, Tt which implies T=kt+c, where 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 dTdt versus t graph.

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