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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.)

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  1. 23 June, 11:12
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    (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
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