Question

Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species and the air temperature. When the temperature is 60°F, the crickets chirp at the rate of 80 chirps/min, and when the temperature is 80°F, they chirp at the rate of 160 chirps/min. (a) Find an equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets. N= (b) Use this function to determine the rate at which the crickets chirp when the temperature is 102 F chirps/min Need Help? Read It

Answer 1

Answer:

a) $y=4x-160$

b) $y=4(102)-160=248\frac{chirps}{min}$

Step-by-step explanation:

We know that theres a linear relationship between the rate of the chirping of crickets and the air temperature.

The equation of a line is:

$y=mx+b$

So, let's name our variables

x= Temperature

y=Rate of the chirping

First of all, we need to find the slope with the two given points

$x_{1}=$60ºF , $y_{1} =80\frac{chirps}{min}$

$x_{2} =$80ºF, $y_{2} =160\frac{chirps}{min}$

By,

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{160-80}{80-60}$

$m=4$

Now, the equation between the air temperature and the number of chirps is:

$y-y_{1} =m(x-x_{1} )$

$y-80=4(x-60)$

Solving for y,

a) $y=4x-160$

b) To calculate the rate at which the crickets chirp when the temperature is 102 ºF we need to evaluate y(102)

$y=4(102)-160=248\frac{chirps}{min}$