Question

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

Answer 1

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.