Applyin​​g the Chain Rule Use the data in Tables 3.4 and 3.5 of Example 4 to estimate the rate of change in pressure with respect to time experienced by the runner when she is at an altitude of 13,330 ft. Make use of a forward difference quotient when estimating the required derivatives.

Verified step by step guidance

1. Identify the variables involved: let P be the pressure and t be the time. We need to find the rate of change of pressure with respect to time, denoted as dP/dt.
2. Locate the relevant data in Tables 3.4 and 3.5 for the altitude of 13,330 ft. Extract the corresponding pressure values and their associated times.
3. Use the forward difference quotient formula to estimate the derivative: dP/dt ≈ (P(t + Δt) - P(t)) / Δt, where Δt is a small increment in time.
4. Substitute the pressure values from the tables into the forward difference quotient formula to compute the estimated rate of change.
5. Interpret the result in the context of the problem, considering how the pressure changes as the runner continues to move at the specified altitude.