Final answer:
The equation expressing air pressure as a function of altitude, assuming a linear relationship, is P(A) = -0.0025A + 14.7. The air pressure in Mexico City at an elevation of 7300 feet would be 11.45 psi. The negative value obtained for the top of Mt. Everest suggests the linear model is not adequate for very high altitudes.
Step-by-step explanation:
Equation Representing Air Pressure as a Function of Altitude
To write an equation expressing air pressure as a function of altitude based on the information given, we can use two data points provided: at sea level, which is 0 feet, the air pressure is approximately 14.7 psi, and in Denver, Colorado, at 5280 feet, the air pressure is approximately 12.15 psi. Assuming the relationship between air pressure and altitude is linear, we can use these two points to construct a linear equation:
To find the air pressure in Mexico City at 7300 feet, we substitute the altitude into the equation: P(7300) = -0.0025(7300) + 14.7, giving us an air pressure of approximately 14.7 - 0.0025(7300) = 14.7 - 18.25 = 11.45 psi. Similarly, for the top of Mt. Everest at 29000 feet, P(29000) = -0.0025(29000) + 14.7, giving us an air pressure of approximately 14.7 - 0.0025(29000) = 14.7 - 72.5 = -57.8 psi. However, this negative value does not make sense physically, indicating that the linear model applied only works for altitudes up to a certain point and that the relationship between air pressure and altitude becomes nonlinear at higher altitudes.