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 113 chirps per minute at 70°F and 173 chirps per minute at 80°F. (a) Find a linear equation that models the temperature T as a function of the number of chirps per minute N.

Answer 1

Answer:

$y=\frac{1}{6}x+\frac{307}{6}$

Step-by-step explanation:

Basically the word problem here is trying to get us to find the line using the two points (113,70) and (173,80).

It also tells us by saying that we're modeling the temperature that we're going to be using the y = mx + b formula. m and b are what we'll mainly be looking for.

Let's start by finding m, the slope. We'll be using the point slope formula:

$\frac{y_2-y_1}{x_2-x_1} \\\frac{70-80}{113-173}\\\frac{10}{60}\\ \frac{1}{6}$

So m = 1/6.

Now let's use that m and choose one of the points (I chose (113,70) ) to plug in everything but b in the original formula

$y=\frac{1}{6} x+b\\70=\frac{1}{6}113+b\\420=113+6b\\307=6b\\\frac{307}{6}=b$

so now that we know our b and our m, we can plug those into the original equation to get our answer!

$y=\frac{1}{6}x+\frac{307}{6}$