Chapter 8.8, Problem 43E

Nonuniform grids Use the indicated methods to solve the following problems with nonuniform grids.

33. A hot-air balloon is launched from an elevation of 5400 ft above sea level. As it rises, its vertical velocity is computed using a device (called a variometer) that measures the change in atmospheric pressure. The vertical velocities at selected limes are shown in the table (with units of ft/min).

1. a. Use the Trapezoid Rule to estimate the elevation of the balloon after five minutes. Remember that the balloon starts at an elevation of 5400 ft.
2. b. Use a right Riemann sum to estimate the elevation of the balloon after five minutes.
3. c. A polynomial that fits the data reasonably well is

$g(t)=3.49t^3-43.21t^2+142.43t-\mathrm{1.75.}$

  Estimate the elevation of the balloon after five minutes using this polynomial.