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

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 times are shown in the table (with units of ft/min).

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.

b. Use a right Riemann sum to estimate the elevation of the balloon after five minutes.

c. A polynomial that fits the data reasonably well is

g(t) = 3.49t³ - 43.21t² + 142.43t - 1.75.

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

t (min) 3.5 1.5 3 4 150 Velocity (ft/min) 100 120 110 90 80