Question

Biologists have observed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 120 chirps per minute at 70°F and 168 chirps per minute at 80°F.

(a) Find the linear equation that relates the temperature t and the number of chirps per minute n.


(b) If the crickets are chirping at 138 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)

Answer 1

A linear relationship between cricket chirp rate and temperature is used to estimate temperature. The linear equation is n = 4.8t - 216, and a chirp rate of 138 chirps per minute corresponds to approximately 74°F.

Step-by-step explanation:

The question deals with finding a linear equation and using it to estimate temperature based on cricket chirp rate. To find the linear equation that relates the temperature t and the number of chirps per minute n, we use the two given points (70,120) and (80,168).

First, calculate the slope (m):
m = (168 - 120) / (80 - 70) = 48 / 10 = 4.8 chirps per minute per degree Fahrenheit.

Next, use the point-slope form to construct the linear equation,
n - 120 = 4.8(t - 70).

Simplify to get the equation in slope-intercept form:
n = 4.8t - 216.

To estimate the temperature when the crickets chirp at 138 chirps per minute,
138 = 4.8t - 216. Solving for t gives:
t = (138 + 216) / 4.8 = 354 / 4.8 ≈ 73.75°F, rounded to 74°F.