Problem 2 The Metrobus Route N6 can take passengers from American University to Farragut Square, a short walk from the White House. However, most of the route down Massachusetts Av- enue is over very rough surfaces. One day, the 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 sur- face. The seats then continue to bounce up and down for a Image credit: wrnata.co. 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 rst 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 rst three bounces. I.\" 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. (0) 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 nd 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