Biologists have observed that the chirping rate of crickets is linearly related to temperature. A cricket produces 120 chirps per minute at 70 F and 168 chirps per minute at 80 F. a) Write a linear equation in slope-intercept form that gives temperature as a function of the number of chirps per minute. Be sure to tell me what your variables stand for. b) What is the temperature if the crickets chirp at 150 chirps per minute? c) Reverse this function to give the number of chirps per minute as a function of temperature.

a)   t = 5/24 c + 45.

b)  76 degrees F.

c)   c = (24/5) t - 216.

Step-by-step explanation:

a)      The rate of temperature change to number of chirps per minute =   (80-70) / (168 - 120)

=   10 / 48 = 5/24.

So we can write the equation as t = 5/24 c + b  where t = temperature, c = number of chirps and b is a constant.

Plugging in the values  t = 70 and c = 120 we can find the value of b:

70 = (5/24) * 120 + b

b = 70 -  5*5

b = 45

So the required equation is

t = 5/24 c + 45.

b)          When   number of chirps is 150:

Temperature t = (5 *150) / 24 + 45

= 76 degrees F.

c)   Reversing the process

t = 5/24 c + 45

5/24 c = t - 45

c =  (24/5) t - 45 * 24/5

c = (24/5) t - 216.