college algebra

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Erin is a biology student. She heard that the number of times a cricket chirps in one minute can be used to find the temperature. In an experiment, she finds that a cricket chirps 40 times per minute when the temp. is 50 degrees(Fahrenheit) and 80 times per minute when the temp. is 60 degrees. Find the temp. when the cricket chirps at 95 times per min.

  • college algebra -

    on the assumption that this relation is linear,
    you can treat this as being given two ordered pairs in the relation, namely
    (40,50 and (80,60), where the first variable is c (chirps) and the second variable is t (time)

    so we are looking for t = mc + b (to resemble the familiar y = mx + b linear equation)

    slope = (60-50)/(80-40) = 10/40 = 1/4

    using m= 1/4 and the point (40,50)

    50 = (1/4)(40) + b

    b = 40

    so you have t = 1/4c + 40
    when c = 95
    t = (1/4)(95) + 40
    = 63.75 degrees

    OR

    draw a straight line, plot the points
    (40,50), (80,60) and (95,t)

    then (t-60).(95-80) = (60-5)/(80-40)
    (t-60)/15 = 1/4
    4t - 240 = 15
    t = 63.75

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