Integrate the concepts from different units in the Advanced Functions course to design a rollercoaster. Your coaster must meet the following conditions.
•The first part of the ride is modelled by a polynomial function. It includes a steep hill that starts at the origin, where the cars obtain their initial energy.
•The second part of the ride is modelled by a sinusoidal function with at least two cycles.
•The third part of the ride is modelled by a rational function that brings the cars back close to the ground.
•The rates of change where one part of the ride meets another part of the ride must not differ by more than 10%.
a)Determine an equation for each part of the ride.
b)Graph all three equations and show how they join each other.
c)Show that the rates of change at the points at which the models join each other do not differ by more than 10%.