Final answer:
To calculate the altitude of Mr. Mole's burrow, we use the linear relationship between time and altitude based on the data provided. We find the slope of -2.4 meters per minute and extrapolate back to when time equals zero, resulting in an altitude of -6 meters.
Step-by-step explanation:
Calculating the Altitude of Mr. Mole's Burrow
To determine the altitude of Mr. Mole's burrow, we need to analyze the provided data on his digging progress and apply our understanding of linear equations. From the information given, Mr. Mole digs at a constant rate, which suggests that we can use a linear relationship between time and altitude. The data points provided are as follows: At 6 minutes, the altitude is -20.4 meters; at 9 minutes, it is -27.6 meters; and at 12 minutes, it is -34.8 meters.
First, we calculate the slope of the line, which represents the rate at which Mr. Mole is digging. The slope (m) is found by taking the difference in altitude divided by the difference in time between any two points. Let's use the 6-minute and 9-minute marks:
Slope (m) = (Altitude at 9 minutes - Altitude at 6 minutes) / (Time at 9 minutes - Time at 6 minutes)
m = (-27.6 - (-20.4)) / (9 - 6)
m = (-27.6 + 20.4) / 3
m = -7.2 / 3
m = -2.4 meters per minute
Now, to find the altitude of Mr. Mole's burrow, which corresponds to time = 0, we extrapolate back using the slope. Using the point-slope form of the linear equation, y - y1 = m(x - x1), where y1 is -20.4 meters, x1 is 6 minutes, and m is -2.4 meters per minute, we plug in x = 0 to solve for y, the altitude at time = 0.
y - (-20.4) = -2.4(0 - 6)
y + 20.4 = -2.4(-6)
y + 20.4 = 14.4
y = 14.4 - 20.4
y = -6 meters
The altitude of Mr. Mole's burrow is -6 meters. This is the answer you will mention as the correct option in your final answer, and you should choose only this one option as it is derived from the calculation.