Question

Entomologists are biological scientists who study insects. Entomologists studying tree

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.