Chapter 1.2, Problem 17E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 70°F and 173 chirps per minute at 80°F.

(a) Find a linear equation that models the temperature T as a function of the number of chirps per minute *N*.

(b) What is the slope of the graph? What does it represent?

(c) If the crickets are chirping at 150 chirps per minute, estimate the temperature.

(a)

To determine

**To find:** The linear equation of the temperature in terms of the number of chirps per minute *N*.

Explanation

Let *T* be the temperature in *F* and the *N* be the number of chirps produced per minute.

Recall that the general equation of the linear function
*m* is the slope and *c* is the *y*-intercept.

Since the function follows the linear function, the equation of the temperature in terms of *N* is in the form of

According to the given data,

When *N* = 113, the temperature is 70°*F* which can be expressed as (113, 70).

When *N* = 173, the temperature is 80°*F* which can be expressed as (173, 80).

Using these two points, the slope *m* is obtained as follows.

Thus, the slope

Use the slope
*T* in terms of *N* as follows

(b)

To determine

**To find:** The slope of the graph of the temperature function and interpret the slope.

(c)

To determine

**To find:** The temperature if the chirps are produced at the rate of 150 per minute.

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