Question

: In an article published in the American Naturalist in November 1897, A. E. Dolbear wrote about his findings concerning crickets chirping and the temperature of the environment. He wrote, “The rate of chirp seems to be entirely determined by the temperature and this to such a degree that one may easily compute the temperature when the number of chirps per minute is known.” Also, “Below a temperature of 50°[F] the cricket has no energy to waste in music and there would be but 40 chirps per minute.” He presented the following data. At 60 °F, the rate is 80 chirps per minute and at 70 °F, the rate is 120 chirps per minute.

1. Design a table and record the pertinent values in the problem statement. ( 1 2 3 4 5 ) (5.5 pts)

2. Assume there is a linear relationship between the chirping rate, N, and the temperature T; make a sketch of a linear graph for the data in your table, with T on the y-axis and N on the x-axis. ( 1 2 3 4 5 ) (3.5 pts)

3. Using your graph, calculate the equation that gives the temperature as a function of the chirping rate. ( 1 2 3 4 5 ) (3.5 pts)

4. Using the equation that you derived above, calculate chirping rate you would expect to hear if the temperature was 59 °F. ( 1 2 3 4 5 ) (2.5 pts)

5. The Library of Congress (LOC) website (http://www.loc.gov/rr/scitech/mysteries/cricket.html) made the following observation, “To get a rough estimate of the temperature in degrees Fahrenheit, count the number of chirps in 15 seconds and then add 37. The number you get will be an approximation of the outside temperature.”

Write an equation (the LOC’s equation) for the approximation equation for the temperature from what you understand from the statement given by the LOC’s website. ( 1 2 3 4 5 ) (2.5 pts)

6. Calculate the chirping rate (in chirps per minute) using your LOC’s equation for the temperature of 59 °F. ( 1 2 3 4 5 ) (3.5 pts)

7. Write a few sentences (no less than three sentences) to let me know how you would reconcile any difference between the chirping rate you calculated from the equation you derived and that calculated from the LOC’s equation. ( 1 2 3 4 5 ) (4.5 pts)

Answer 1