A bus hits a bump in the road, raising the back row seats by 16 inches above their regular position of two feet above the road surface. The seats then continue to bounce up and down fora few seconds, with each bounce lasting a full second. A. Use the information above to give a trigonometric model for the height of the seats above the road, as a function of the time since the peak of the first bump. B. Due to the hard-working shock absorbers in the bus, each bounce is less severe than the one before. The table below gives the height above the usual seat position for the first three bounces.

Show that the data in this table can represent an exponential function and use the table to give an exponential function for the amplitude of the bounce as a function of time. C. Combine the functions from parts (a) and (b) so that the exponential function is-substituted for the amplitude in the trigonometric model. Use this function to find how long it will take for the peak of each bounce to be less than 0.1 inches from the original-height of the seats.