More than mere folklore, it is a biological fact that crickets chirp more when it is hot. For the snowy tree cricket (Oecanthus fultoni), the relationship between the chirp rate and the temperature is so reliable that it is referred to as the thermometer cricket. You can get a very close estimate of the temperature (in degrees Fahrenheit) by counting the number of times a snowy tree cricket chirps in fifteen seconds and adding 40.
The rule used to estimate the temperature T (°F) in terms of the chirp rate, R (in chirps per minute) is an example of a function. The chirp rate is the independent variable in this situation, and the temperature is the dependent variable, since it is is determined by the chirp rate.
Describe this function using words, a table, a graph, and a formula.
Use what you know, and the graphing calculator, to answer the following questions:
- For what range of temperatures do you think this relation is valid?
- This situation describes a linear function. What is the meaning of the slope and intercepts?
- Last night was warm and muggy. I heard the temperature was still 75° at midnight! How many times would I expect the snowy tree cricket to have chirped in a minute?
- I remember being on vacation in Vermont last year and counting 15 chirps in 15 seconds one night. What month do you think I took that vacation?