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?
Select an answer​

Answer 1

Answer:

$C(T) = 0, T \leq 45\\~~~~~~~~= 3.6T - 162, T > 45$

Cricket will make 198 chirps per minute when temperature is 100 degrees.

Step-by-step explanation:

We are given the following in the question:

a) The number of chirps per minute, C, that the tree cricket makes is linearly dependent on  the temperature, T, in Fahrenheit.

Let this relation be given by the linear equation:

$C(T) = aT + b$

where a and b are constants.

The crickets do not chirp at all below 45 degrees.

$C(T) = 0, T \leq 45\\~~~~~~~~= aT + b, T > 45$

When the temperature is 45 degrees, C(T) = 0

Thus, we can write,

$0 = 45a + b$

At 85 degrees they chirp about 144 times per minute.

$144 = 85a + b$

Solving the equation, we get,

$144-0 = 40a\\\\a = \dfrac{144}{40} = 3.6\\\\144 = 85(3.6) + b\\b = -162$

$C(T) = 0, T \leq 45\\~~~~~~~~= 3.6T - 162, T > 45$

b) chirps per minute will crickets make at 100 degrees

We put T = 100 in the above equation,

$C(T) = 3.6(100) -162 = 198$

Cricket will make 198 chirps per minute when temperature is 100 degrees.