Biologists have observed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear.

Question

A cricket produces 120 chirps per minute at 70°F and 168 chirps per minute at 80°F.

A) Find the linear equation that relates the temperature t and the number of chirps per minute n.

B) If the crickets are chirping at 144 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)

Answer 1

To find the linear equation, we first need to determine variables. Let's put the number of chirps as "y" and the temperature as "x." This will give us two coordinates, (70,120) and (80,168).

Now we need to find the linear equation. To do this, we will use point-slope formula. First we will need to determine the slope:

y₂ - y₁ . 168 - 120 . 48 slope = 4.8

x₂ - x₁ . 80 - 70 . 10

Now that we know the slope, we can plug the slope and one of the coordinates into point-slope formula. I will use the first point, (70, 120).

y - y₁ = m (x - x₁)

y - 120 = 4.8 (x - 70)

y - 120 = 4.8x - 336

Add 120 to both sides

y = 4.8x -216

To solve the second question, plus 144 in for y and solve for x.

144 = 4.8x - 216

Add 216 to both sides

360 = 4.8x

Divide both sides by 4.8

x = 75, so the answer is 75 degrees

Answer 2

(a) n = 4.8*t - 216

(b) @ n = 144 chirps/min, t = 75 degF