Expert: Sherman D. - 4/16/2004

Question
Biologists have observed 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 120 chirps per minute at 70 degrees fahrenheit and 168 chirps per minute at 80 degrees fahrenheit.

a) Graph the data.

b) Express temperature as a function of chirping rate.

c) If the cricket is chirping at 150 chirps per minute, estimate the temperature.  

Answer
(120,70)(168,80)

m = (y2 - y1)/(x2 - x1)
m = (80 - 70)/(168 - 120)
m = (10)/(48)
m = (5/24)

y1 = mx1 + b

70 = (5/24)(120) + b
70 = 25 + b
b = 45

y = (5/24)x + 45

a.) For a graph, go to www.calculator.com, click Graphing, then type in only "(5/24)x + 45", exactly like that, except for the quotation marks, also make sure to leave out the y = part.

b.) T(r) = (5/24)x + 45

c.)
T(150) = (5/24)(150) + 45
T(150) = 31.25 + 45
T(150) = 76.25°F