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 below 45 degrees and
at 85 degrees they chirp about 144 times per minute.
A) Express the number of chirps, C, as a function of the temperature, T. Be sure to use
function notation.
B) How many chirps per minute will crickets make at 100 degrees?

Answer 1

Answer:

Step-by-step explanation:

Given that Entomologists are biological scientists who study insects. Entomologists studying tree  crickets have found that they chirp at different rates depending on the temperature.

At 45 degrees chirp is 0 and at 85 degrees chirp is 144 times

If we fix temperature on x axis and no of chirps on y axis we have two points as

(45,0) and (85,144)

Since linear relationship is given, we use two point formula

$\frac{x-45}{85-45} =\frac{y-0}{144-0} \\144(x-45)=40y\\ 18(x-45)=5y\\18x-5y = 810$

is the linear relation

Or $C= \frac{18T-810}{5}$, for T≥45

B) when T = 100, we have

C = $\frac{1800-810}{5} =198$

Answer 2

A function representing the situation is required, and the chirps per minute at 100 degrees is required.

The required function is

$C(T)=\left\{\begin{matrix}0, & T\leq45 \\ 3.6T-162, & T>45\end{matrix}\right.$

The number of chirps at 100 degrees is 198 chirps per minute.

Less than or at 45 degrees there is no chirping.

At 85 degrees the chirping rate per minute is 144.

The two ordered pairs are

$(45,0),(85,144)$

The equation will be

$C-0=\dfrac{144-0}{85-45}(T-45)\\\Rightarrow C=3.6(T-45)\\\Rightarrow C=3.6T-162$

The required function is

$C(T)=\left\{\begin{matrix}0, & T\leq45 \\ 3.6T-162, & T>45\end{matrix}\right.$

At $T=100$

$C(100)=3.6\times 100-162\\\Rightarrow C(100)=198$

The number of chirps at 100 degrees is 198 chirps per minute.

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