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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

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 y=mx+c where 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 T=mN+c .

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.

m=8070173113=16

Thus, the slope m=16 .

Use the slope m=48 , any one the two point say (113, 70) and obtain the equation of temperature 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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