Question

The number of chirps per minute, C, that the tree cricket makes is linearly dependent on the temperature, T, in Fahrenheit. The crickets do not chirp at all at 44 degrees and at 74 degrees they chirp about 105 times per minute.

A) Express the number of chirps, C, in terms of the temperature, T.
C
=
C
=

B) How many chirps per minute will crickets make at 80 degrees?

Answer 1

(A) C = 3.5(T -44)

(B) 126 chirps/minute

Explanation:

A)

The rise in chirps per minute is (105 -0) = 105 over a temperature increase of (74 -44) = 30 °F. Then the slope of the linear relation is ...

slope = rise/run = 105/30 = 3.5

In point-slope form, the equation for the number of chirps could be ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

C = 3.5(T -44) . . . . line with slope 3.5 through point (T, C) = (44, 0)

__

B)

For T=80, the relation predicts a chirp rate of ...

C = 3.5(80 -44) = 3.5(36) = 126

The crickets are predicted to make 126 chirps per minute at 80 °F.