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

a)
`y=4x-160`

b)
`y=4(102)-160=248(chirps)/(min)`

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(chirps)/(min)`

`x_(2) =`80ºF,
`y_(2) =160(chirps)/(min)`

By,

`m=(y_(2)-y_(1)  )/(x_(2)-x_(1)  ) =(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(chirps)/(min)`