   Chapter 12.1, Problem 53E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Wind chill When the air temperature is 20° F , the rate of change of the wind chill temperature t ( °F ) is given by d t d w = − 4.352 w − 0.84 where w is wind speed in miles per hour.(a) Will both the rate of change of wind chill temperature and wind chill temperature decrease as the windspeed increases? Explain.(b) If the wind chill temperature is 1°F when the wind speed is 31 mph and the air temperature is 20°F , find the function that models the wind chill temperature.

a)

To determine

Whether both the wind chill temperature and rate of change of wind chill temperature decreases if there is a decrease in wind speed and the rate of change of the wind chill temperature t(°F) at air temperature 20°F is dtdw=4.352w0.84

Explanation

Given Information:

Rate of change of the wind chill temperature t(°F) at air temperature 20°F is

dtdw=4.352w0.84

Explanation:

Consider the provided data,

Rate of change of the wind chill temperature t(°F) at air temperature 20°F is

dtdw=4.352w0.84

As, w is the wind speed in miles per hour therefore w0

And if w0

Then, dtdw0

So, dtdw0

This means that there is an inverse relation between the wind chill temperature and speed of wind

As the wind speed decreases the wind chill temperature will increase

b)

To determine

To calculate: The function modelling the wind chill temperature if the wind speed is 31 mph, the wind chill temperature is 1°F and the rate of change of the wind chill temperature t(°F) at air temperature 20°F is dtdw=4.352w0.84

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