Function Word Problem?
a) Express the number of chirps (C) as a function of the temperature (t).
Ok so so far I know this:
C = chirps per min
t = temperature
(t,C)
(40,0) (80, 168)
(168-0)/(80-40)
168/40
4.2
Now what though? I don’t know how to get from that to the equation C(t) = 4.2t – 168. What does the 4.2 stand for and why do you subtract the 168? Help!!!
Thanks!
Favorite Answer
168 is the number of chirps in 40 degrees. You know that the cricket will not chirp until the temperature hits 40. So subtracting the 168 compensates for the 0 degrees to 40 degrees. Otherwise the number would inflated.
y = mx+b.
In this case, chirps (C) = 4.2t plus some constant, and that constant is the y intercept of the equation — the place where x is 0.
Hmmm…what’s that constant? Well, in the slope-intercept form of the equation, just plug in the numbers you already have. Choose the point 40,0, which you know is on the line. 0 = 4.2(40) + b, so 0 = 168 + b and b = -168.
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