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Alina [70]
3 years ago
11

Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species an

d 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
Mathematics
1 answer:
vekshin13 years ago
5 0

Answer:

a) y=4x-160

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

Step-by-step explanation:

We know that theres a <u><em>linear relationship</em></u> between the rate of the chirping of crickets and the air temperature.

<u><em>The equation of a line is</em></u>:

y=mx+b

So, let's name our variables

x= Temperature

y=Rate of the chirping

First of all, we need to find the <u><em>slope</em></u> 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

<u>Now, the </u><em><u>equation</u></em><u> between the air temperature and the number of chirps is:</u>

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

y-80=4(x-60)

Solving for y,

a) y=4x-160

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

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

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