# Solving Linear Function: Temperature & Chirp Rate

• physics604
In summary: It gives 77.2 as the temperature at 150 chirps per minute, which is closer to the textbook answer of 76°F than the calculated -26°F. So the textbook is most likely correct.

#### physics604

I know how to do this question, but I'm trying to figure out if the textbook answer is wrong. This is from James Stewart's Calculus Early Transcendentals, 7th edition.

1. Biologists have noticed 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 113 chirps per minute at 70°F and 173 chirps per minute at 80°F.

(a) Find a linear equation that models the temperature T as a function of the number of chirps per minute N.
(b) What is the slope of the graph? What does it represent?
(c) If the crickets are chirping at 150 chirps per minute, estimate the temperature.

y=mx+b

## The Attempt at a Solution

a) The question wants T as a function of time (don't ask me why it's weird like that), so I know my equation has to be T=mN+b. After punching (113,70) and (173,80) into my calculator, I get y=1/6N-307/6. This is what the textbook had. Great. Please keep going.

b) Slope is 1/6, easy. It represents change in for every chirp per minute change. This was right. Please read on one more.

c) It wants the temperature when N=150. The problem is, using the equation, the temperature would be about -26°F. The textbook said this was wrong. Their answer was 76°F. The only way you can get 76 as an answer is if your initial equation was y=6N-307 (I know because I used this equation first).

Am I right? Is the textbook wrong?

physics604 said:
I know how to do this question, but I'm trying to figure out if the textbook answer is wrong. This is from James Stewart's Calculus Early Transcendentals, 7th edition.

1. Biologists have noticed 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 113 chirps per minute at 70°F and 173 chirps per minute at 80°F.

(a) Find a linear equation that models the temperature T as a function of the number of chirps per minute N.
(b) What is the slope of the graph? What does it represent?
(c) If the crickets are chirping at 150 chirps per minute, estimate the temperature.

y=mx+b

## The Attempt at a Solution

a) The question wants T as a function of time (don't ask me why it's weird like that), so I know my equation has to be T=mN+b. After punching (113,70) and (173,80) into my calculator, I get y=1/6N-307/6. This is what the textbook had. Great. Please keep going.
You mean chirp rate, N, not time.

b) Slope is 1/6, easy. It represents change in for every chirp per minute change. This was right. Please read on one more.

c) It wants the temperature when N=150. The problem is, using the equation, the temperature would be about -26°F. The textbook said this was wrong. Their answer was 76°F. The only way you can get 76 as an answer is if your initial equation was y=6N-307 (I know because I used this equation first).
Show your work. You're either setting the problem up wrong or solving for T incorrectly.

Am I right? Is the textbook wrong?
The text appears to be right.

physics604 said:
a) so I know my equation has to be T=mN+b. After punching (113,70) and (173,80) into my calculator, I get y=1/6N-307/6. This is what the textbook had. Great. Please keep going.

If y=T, the equation is wrong. It has to be y=1/6 N+307/6, that is T=1/6 N+307/6, or

N=6T-307.

ehild

You can always check c) from the OP by doing linear interpolation on the two data points given.