Final answer:
The boiling point-altitude relationship can be expressed using a linear equation. The boiling point of the liquid can be calculated using the equation b = -0.0052a + 246.4, where a is the altitude in ft and b is the boiling point in °F. The boiling point at an altitude of 2100 ft is 235.2 °F.
Step-by-step explanation:
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 202.4 °F. At the altitude of 4600 ft, the liquid boils at 207.64 °F. To find the boiling point (b) of the liquid in °F, in terms of altitude (a) in ft/°F, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the given altitudes and boiling points, we can calculate the slope:
m = (boiling point at 4600 ft - boiling point at 8100 ft) / (altitude at 4600 ft - altitude at 8100 ft)
m = (207.64 °F - 202.4 °F) / (4600 ft - 8100 ft)
m = -0.0052 ft/°F
Now, we can substitute the slope and the boiling point at 8100 ft into the equation to find the y-intercept:
202.4 °F = -0.0052 ft/°F * 8100 ft + b
b = 246.4 °F
Therefore, the equation giving the boiling point (b) of the liquid in terms of altitude (a) is b = -0.0052a + 246.4. To find the boiling point at 2100 ft, we can substitute a = 2100 ft into the equation:
b = -0.0052 * 2100 + 246.4
b = 235.2 °F