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

Question

A cricket produces 119 chirps per minute at 74 degrees Fahrenheit and 170 chirps per minute at 81 degrees Fahrenheit. 

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

(b) If the crickets are chirping at 156 chirps per minute, estimate the temperature:

Answer 1

a)

T(N) = mN+b

T(119) = 119m+b = 74

T(170) = 170m+b = 81

Subtracting the first equation from the first

51m = 7

m = 7/51

(7/51)(170)+b = 81

b = 81 - 23.33 =57.67

T(N) = (7/51)N+57.67

b)

T(156)=(7/51)(156)+57.67 ≈ 79.1° F