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.)

Question

Conner Duncan

Mathematics

23 June, 10:59

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.)

+1

Answers (1)

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Adelyn Orr · 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