Question

Biologists have observed 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 120 chirps per minute at 70°F and 168 chirps per minute at 80°F.
(a) Find the linear equation that relates the temperature t and the number of chirps per minute n.


(b) If the crickets are chirping at 138 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)

Answer 1

(a) Find the linear equation that relates the temperature t and the number of chirps per minute n.
If the equation is linear, then the equation should have the form of t = mn + b

m = (80 - 70) / (168 - 120) = 5/24

t = 5/24n + b

70 = 5/24(120) + b
b = 45

t = 5/24 n + 45

(b) If the crickets are chirping at 138 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)
t = 5/24 n + 45
t = 5/24 (138) + 45 = 74 °F