ntomologists 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 145 chirps/min, and when the temperature is 90°F, they chirp at the rate of 295 chirps/min.(a) Find an equation giving the relationship between the air temperature x and the number of chirps per min y of the crickets.(b) Use this function to determine the rate at which the crickets chirp when the temperature is 101°F.chirps/min

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Asked Sep 5, 2019
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ntomologists 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 145 chirps/min, and when the temperature is 90°F, they chirp at the rate of 295 chirps/min.

(a) Find an equation giving the relationship between the air temperature x and the number of chirps per min y of the crickets.


(b) Use this function to determine the rate at which the crickets chirp when the temperature is 101°F.
chirps/min
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Expert Answer

Step 1

Part A

When the temperature is 60°F, the crickets chirp at the rate of 145 chirps/min, and when the temperature is 90°F, they chirp at the rate of 295 chirps/min.

Let x represents the air temperature and y represents chirps rate.

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Let (x1, y) be (60,145) and (x2, y2) be (90,295) y2-y1 Slope m x2-x1 295-145 90-60 150 30 5 Ln

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Step 2

Finding the equation using the slope-point form i.e.

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у — У1 — т(х — х) Now putting the value of x1 and yin the above equation, get we у — 145 — 5(х — 60) — 300 у — 145 3D 5х 5х — у %3D 300 — 145 5х — у — 155 у %3 5х — 155 Therefore, an equation giving the relationship between the air temperature x and the number of chirps per min y of the crickets is y = 5x - 155

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Step 3

Part b

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101°F then y = 5 x 101 - 155 350. When x

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Algebra

Equations and In-equations