5. Crickets make chirping sounds by rubbing their wings together. The number of chirps they make is closely related to the temperature of their environment. When the temperature is between 55 and 100 degrees Fahrenheit, we can tell the temperature by counting the number of chirps! A formula that is commonly used to find the temperature in degrees Fahrenheit is: Count the number of chirps in 14 seconds, and then add 40 to get the temperature. Let n be the number of chirps that crickets make in 14 seconds and F be the temperature in degrees Fahrenheit. a. What is the temperature when a cricket chirps 52 times in 14 seconds? b. Write an equation that defines F as a function of n. c. How many chirps would we expect to hear in 14 seconds when it is 60 degrees Fahrenheit?
Added by Michael D.
Close
Step 1
So, F = 52 + 40 = 92 degrees Fahrenheit. b. The equation that defines F as a function of n is F(n) = n + 40. Show more…
Show all steps
Your feedback will help us improve your experience
Jason Horton and 92 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The rate at which crickets chirp depends on the ambient temperature, because crickets are cold-blooded insects whose body temperature follows the temperature of their environment. It has been found that the Celsius temperature can be estimated by counting the number of chirps in 8 seconds and then adding 4 . In other words, $t_{\mathrm{C}}-($ number of chirps in 8 seconds $)+4$. (a) Calculate the number of chirps in 8 seconds for temperatures of $20,25,30$, and $35^{\circ} \mathrm{C}$. (b) The number of chirps per unit of time is directly proportional to the rate constant for a biochemical reaction involved in the cricket's chirp. On the basis of this assumption, make a graph of $\ln ($ chirps in $8 \mathrm{~s}$ ) versus $(1 / T) .$ Calculate the activation energy for the biochemical reaction involved. (c) How many chirps would a cricket make in 8 seconds at a temperature of $40^{\circ} \mathrm{C}$ ?
Sri K.
Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. Let the number of chirps be C and the temperature in degrees Fahrenheit be F. a) Find an equation for the line that models this situation. b) How warm is it when the crickets are chirping 150 times a minute? c) Identify the slope, C-intercept, and F-intercept. d) Interpret the meaning of slope, C-intercept, and F-intercept. e) Sketch the calculated equation.
Suzanne W.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD