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23 February, 09:52

According to Dolbear's law, you can predict the temperature T (in degrees Fahrenheit) by counting the number x of chirps made by a snowy tree cricket in 1 minute. For each rise in temperature of 0.25°F, the cricket makes an additional chirp each minute. a. A cricket chirps 40 times in 1 minute when the temperature is 50°F. Write an equation in slope-intercept form that represents the temperature in terms of the number of chirps in 1 minute. equation: T = _ b. You count 100 chirps in 1 minute. What is the temperature? The temperature is_ ºF. c. The temperature is 96 °F. How many chirps would you expect the cricket to make? _chirps

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  1. 23 February, 10:14
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    Short answer T = n/4 + 40; 100 chirps = 65oF; 96o F = 224 chirps.

    Comment

    You have to find the base temperature (the y intercept) where there are no chirps. Then you have to use 1 chirp = 0.25oF

    Givens

    50oF = 40 chirps

    1 chirp = 0.25oF

    Discussion and development of the formula

    That implies that the base temperature was 10 degrees lower, because for every chirp increase per minute the temperature increases 0.25oF

    1 chirp = 0.25oF

    40 chiprs = x Cross multiply

    1*x = 0.25 * 40

    x = 10oF

    So the base temperature or the y intercept is 40oF

    So far what you have is

    T = n + 40 Where n is the number of chirps you hear. Now at 50oF which is 10oC more, you get 40 chirps. So n has to be divided by 4 (for the 0.25oF)

    T = n/4 + 40

    Where n is the number of chirps per minute.

    Now try the samples with our formula.

    Problem one

    n = 100 chirps per minute

    T = 100/4 + 40

    T = 25 + 40

    T = 65 oF

    Problem Two

    T = 96

    n = ?

    96 = n/4 + 40 Subtract 40 from both sides.

    96 - 40 = n/4

    56 = n/4 Multiply by 4

    224 = n

    You would expect 224 chirps / minute

    Very interesting theorem. You can search the internet to find out how this was used on the Big Bang Theory.
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