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
c(t)=\frac{21}{5}(t - 40) for tgeq40
enter your answer using function notation.
b. how many chirps per minute will crickets make at 90 degrees? 210
chirps per minute
part 2 of 2
c. interpret the meaning of the slope in the answer to part a.
when the select an answer select an answer select an answer select an answer, then the select an answer select an answer 4.2 select an answer.
question help: video message instructor

Explanation:

Step1: Find the slope

We have two points $(T_1,C_1)=(40,0)$ and $(T_2,C_2)=(70,126)$. The slope $m$ of the linear - function $C(T)$ is given by the formula $m=\frac{C_2 - C_1}{T_2 - T_1}=\frac{126-0}{70 - 40}=\frac{126}{30}=\frac{21}{5}=4.2$. Using the point - slope form $C - C_1=m(T - T_1)$ with $(T_1,C_1)=(40,0)$ and $m = \frac{21}{5}$, we get $C(T)=\frac{21}{5}(T - 40)$ for $T\geq40$.

Step2: Calculate chirps at 90 degrees

Substitute $T = 90$ into the function $C(T)=\frac{21}{5}(T - 40)$. Then $C(90)=\frac{21}{5}(90 - 40)=\frac{21}{5}\times50=210$.

Step3: Interpret the slope

The slope of the function $C(T)=\frac{21}{5}(T - 40)$ is $\frac{21}{5}=4.2$. In the context of the problem, when the temperature ($T$) increases by 1 degree Fahrenheit, then the number of chirps per minute ($C$) increases by 4.2.

Answer:

A. $C(T)=\frac{21}{5}(T - 40)$ for $T\geq40$
B. 210
C. When the temperature increases by 1 degree Fahrenheit, then the number of chirps per minute increases by 4.2.