Function Word Problem?

The number of chips per minute (C) that the cricket makes is linearly dependent on the temperature (t) in Fahrenheit. The crickets did not chirp at all at 40 degrees and at 80 degrees they chirp about 168 times a minute.

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!

Top 2 Answers

A few days ago

sarure

Favorite Answer

The slope, 4.2, is the additional number of times that the cricket will chirp everytime the temperature increases one degree.

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.

A few days ago

historian

Good work so far. The 4.2 is the slope of the line. In this case, it’s the number of extra chirps (the y or dependent variable) for every increase of 1 in the temperature (the x or independent variable).

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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