Final answer:
The linear equation that relates temperature to the number of cricket chirps per minute is n = 4.8t - 216. Using this equation, an estimate of the temperature for a cricket chirping at 144 times per minute is approximately 75°F.
Step-by-step explanation:
The question asks for a linear equation that relates the temperature t and the number of chirps per minute n for a cricket. Given the data: at 70°F, the cricket chirps 120 times per minute, and at 80°F, it chirps 168 times per minute, we can find the slope (m) using the formula (n2 - n1) / (t2 - t1).
m = (168 - 120) / (80 - 70) = 48 / 10 = 4.8 chirps/minute per degree. Now, using one of the points and the slope, we can find the y-intercept (b) of the linear equation n = mt + b.
Using the point (70, 120): 120 = 4.8 * 70 + b; thus b = 120 - (4.8 * 70) = 120 - 336 = -216. So, our linear equation is n = 4.8t - 216.
Now to estimate the temperature (t) for 144 chirps per minute, we set n to 144 and solve for t: 144 = 4.8t - 216; 4.8t = 144 + 216; t = (144 + 216) / 4.8; after calculating, the temperature is approximately 75°F.