Question

Biologists have noticed that the chirping of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 112 chirps per minute at 74 degrees Fahrenheit and 179 chirps per minute at 82 degrees Fahrenheit..

Answer 1

Answer:

$T(N)=\frac{67}{8}N-\frac{2031}{4}$

Step-by-step explanation:

Please consider the complete question.  

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 112 chirps per minute 74° F at and 179 chirps per minute at 82°F. Find a linear equation that models the temperature T as a function of the number of chirps per minute N.

We have been given two points on the line $(74,112)$ and $(82,179)$.

First of all, we will find the slope of the line using given points as:

$\text{Slope}=m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{179-112}{82-74}$

$m=\frac{67}{8}$

Now, we will points-slope form of an equation to write our required equation as:

$(y-y_1)=m-(x-x_1)$

$(y-112)=\frac{67}{8}-(x-74)$

$(y-112)=\frac{67}{8}(x-74)$

$y-112=\frac{67}{8}x-\frac{67}{8}*74$

$y-112+112=\frac{67}{8}x-\frac{67}{8}*74+112$

$y=\frac{67}{8}x-\frac{67}{4}*37+\frac{4*112}{4}$

$y=\frac{67}{8}x-\frac{2479}{4}+\frac{448}{4}$

$y=\frac{67}{8}x-\frac{2031}{4}$

Since we are required to write temperature T as a function of the number of chirps per minute N, so we will get:

$T(N)=\frac{67}{8}N-\frac{2031}{4}$

Therefore, our required function would be  $T(N)=\frac{67}{8}N-\frac{2031}{4}$.