Question

Biologists have noticed that the chirping of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 111 chirps per minute at 74 degrees Fahrenheit and 173 chirps per minute at 87 degrees Fahrenheit.

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

B) If the crickets are chirping at 158 chirps per minute, estimate the temperature:
Temperature =

Answer 1

A) T = 13/62N +(50 45/62)

B) T ≈ 83.9 °F

Explanation:

A)

The equation can be written in slope-intercept form by finding the slope (m) and the y-intercept (b). The formulas are ...

m = (y2 -y1)/(x2 -x1)

b = y1 -m(x1)

For the given points (111, 74) and (173, 87), the slope is ...

m = (87 -74)/(173 -111) = 13/62

The y-intercept is ...

b = 74 -(13/62)(111) = 50 45/62

Then the equation in slope-intercept form is ...

y = mx +b

T = 13/62N +(50 45/62)

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B)

For a chirp rate of N=158, the temperature is approximately ...

T = (13/62)(158) +(50 45/62) = 33 8/62 +50 45/62 = 83 53/62

T ≈ 83.9 °F