   Chapter 2.3, Problem 47E

Chapter
Section
Textbook Problem

Cricket Chirping and Temperature Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is 70°F. the crickets chirp at the rate of 120 times/min. and when the temperature is 80°F. they chirp at the rate of 160 times/min. a. Find an equation giving the relationship between the air temperature T and the number of chirps per minute, N, of the crickets. b. Find N as a function of T, and use this formula to determine the rate at which the crickets chirp when the temperature is 102°F.

(a)

To determine
The equation that gives the relationship between the air temperature and number of crickets chirp per minute.

Explanation

Given:

Entomologists have discovered a linear relationship between number of chirps of crickets of certain species and the air temperature. When the temperature is 70°F , the crickets chirps at the rate of 120 times/min, and when the temperature is 80°F , they chirp at the rate of 160 times/min.

Formula used:

The equation of a straight line passes through point (x1,y1) and have slope m is

(yy1)=m(xx1) (1)

Slope m of a line for two points (x1,y1) and (x2,y2) is,

m=y2y1x2x1 (2)

Calculation:

The number of chirps of crickets and air temperature has a linear relationship, so the coordinate becomes (70,120) and (80,160) .

Substitute 70 for x1 , 120 for y1 , 80 for x2 and 160 for y2 in equation (2) to evaluate the value of m

(b)

To determine
The rate at which cricket chirps when the temperature is 102°F

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