Question

entomologists are biological scientists who study insects. entomologists studying tree crickets have found that they chirp at different rates depending on the temperature. the number of chirps per minute, c, that the tree cricket makes is linearly dependent on the temperature, t, in fahrenheit. the crickets do not chirp at all at 40 degrees and at 70 degrees they chirp about 126 times per minute. a. express the number of chirps, c, as a function of the temperature, t for t ≥ 40 enter your answer using function notation. b. how many chirps per minute will crickets make at 90 degrees? chirps per minute question help: video message instructor

Explanation:

Step1: Find the slope of the linear - function

We have two points \((T_1,C_1)=(40,0)\) and \((T_2,C_2)=(70,126)\). The slope \(m\) of a line is given by the formula \(m=\frac{C_2 - C_1}{T_2 - T_1}\).

$$m=\frac{126 - 0}{70 - 40}=\frac{126}{30}=\frac{21}{5}$$

Step2: Find the equation of the line

The point - slope form of a line is \(C - C_1=m(T - T_1)\). Using the point \((40,0)\) and \(m = \frac{21}{5}\), we get \(C-0=\frac{21}{5}(T - 40)\), so \(C(T)=\frac{21}{5}(T - 40)\) for \(T\geq40\).

Step3: Calculate the number of chirps at \(T = 90\)

Substitute \(T = 90\) into the function \(C(T)=\frac{21}{5}(T - 40)\).

$$C(90)=\frac{21}{5}(90 - 40)=\frac{21}{5}\times50=210$$

Answer:

A. \(C(T)=\frac{21}{5}(T - 40)\)
B. 210