Question

Biologists have noticed that the chirping of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 73 degrees Fahrenheit and 172 chirps per minute at 87 degrees Fahrenheit.Find a linear equation that models the temperature T as a function of the number of chirps per minute N.T(N)= ?

Answer 1

Answer:

$T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}$

Step-by-step explanation:

We are given the following in the question:

The relation between  chirping of crickets and temperature is a linear function.

$T(N) = aN + b$

where and b are constants. T(N) is the the temperature in Fahrenheit and N is the number of chirps per minute.

"A cricket produces 113 chirps per minute at 73 degrees Fahrenheit"

$73 = 113a+b$

"A cricket produces 172 chirps per minute at 87 degrees Fahrenheit"

$87 = 172a+b$

Solving the two equations, we get,

$87-73 = 172a - 113a\\14 = 59a\\\\a =\dfrac{14}{59}\\\\73 = 113(\dfrac{14}{59}) + b\\\\b = 73 - 113(\dfrac{14}{59})\\\\b = \dfrac{2725}{59}$        

Thus, the required linear function is:

$T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}$