Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68°F. When they chirp 172 times a minute, it is about 80°F. (a) Find an equation for the line that models this situation; (b) How warm is it when the crickets are chirping 160 times a minute?

a) The relation between chirps per minute and temperature is linear, therefore we know that f(x) = mx + b for some m and b. To find the equation that models this, we will need to find m and b.

From the data that the problem gives us we know that the independent variable x is the number of crickets per minute and the dependant variable is the temperature. We know will write down the equations and solve:

68 = 124m + b

80 = 172[tex]b=68 - 124m\\b=80-172m\\\\68-124m=80-172m\\48m=12\\m=0.25\\\\b=68-124m\\b=68-124(0.25)\\b=68-31\\b=37[/tex]m + b.

Therefore the equation would be:

f(x) = 0.25x + 37

b) How warm is it when the crickets are chirping 160 times a minute?

f(160) = 0.25 (160) + 37

f(160) = 40 + 37

f(160) = 77

It will be 77ºF