Question

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?

Answer 1

a) f(x) = 0.25x + 37

b) 77ºF

Explanation:

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
`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`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