Entomologists have discovered that a linear relationship exists between the rate
ID: 2259163 • Letter: E
Question
Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species and the air temperature. When the temperature is 60°F, the crickets chirp at the rate of 80 chirps/min, and when the temperature is 90°F, they chirp at the rate of 200 chirps/min.
(a) Find an equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets.
N =
(b) Use this function to determine the rate at which the crickets chirp when the temperature is 100°F.
chirps/min
Explanation / Answer
a) Let the linear relationship be y=ax+b
when x=60°F,y= 80 chirps/min , implies 80=60a+b --(1)
when x=90°F,y=200 chirps/min, implies 200=90a+b --(2)
from equations (2)-(1) we get
120=30a
a=120/30=4
substitute a=4 into equation (1)
80=60a+b
80=60*4+b
b=80-240=-160
implies y=ax+b
y=4x-160
b)we have linear relationship is y=4x-160
when the temperature is x=100°F
y=4*100-160 sine y=4x-160
=400-160=240
y=240 chirps/min when the temperature is x=100°F
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