The temperature T in degrees Fahrenheit is a linear function of the number C of cricket chirps per minute.

Question

A temperature of 52 degrees Fahrenheit indicates twenty cricket chirps per minute. Each additional chirp per minute corresponds to an increase of 0.25 degrees.

 

1) Use a formula to express T as a linear function of C

 

2) what temperature is indicated by 100 cricket chirps per minute?

 

3)What range of temperature are indicated when there are between 100 and 120 cricket chirps per minute

Answer 1

T is a linear function of C  ==>  T = mC + b  

 

Each additional chirp C corresponds to an increase in T of 0.25  ==>  m = 0.25 

 

T = 52 when C = 20  ==>  52 = 0.25(20) + b  ==>  b = 52 - 5 = 47

 

So T = 0.25C + 47 

 

When C = 100 then T = 0.25(100) + 47 = 25 + 47 = 72

 

When C = 120 then T = 0.25(120) + 47 = 30 + 47 = 77 so the temperature range is between 72 and 77 when there are between 100 and 120 chirps per minute