Please provide a step by step Biologists have noticed that the chirping rate of

Question

Please provide a step by step

Biologists have noticed that the chirping rate 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 70°F and 163 chirps per minute at 80°F (a) Find a linear equation that models the temperature Tas a function of the number of chirps per minute N (b) What is the slope of the graph? What does it represent? The slope means that the temperature in Fahrenheit degrees increases as rapidly as the number of cricket chirps per minute. (c) If the crickets are chirping at 110 chirps per minute, estimate the temperature. (Round your answer to the nearest whole number.) OF

Explanation / Answer

From the given question,

a) If N= number of chirps per minute, T=temperature

Let the linear function be T=aN+b

when N=113, T=70           

70=113a+b ............(1)

when N=163,T=80            

80=163a+b ............(2)

(2) - (1)

10=50a

a=0.2

70=113(0.2)+b

b=47.4

T=0.2N+47.4

slope of the graph is 0.2

The slope means that the temperature in Fahrenheit degrees increases 0.2 as rapidly as the number of cricket chirps per minute.

c) If N=110, T= 0.2*110+47.4

T=69.4 F

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