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
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.
