Hi, can you please help me with this math project I have to graph a rollercoaster

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.

 Your curve must pass through the point (5, 15)

 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 functions may not connect at a local maximum or minimum point.

 The dimensions of the roller coaster must be realistic. (Max possible height: 90metres)

 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. Label the points of

intersection with their coordinates. The horizontal axis should be horizontal

distance. The vertical axis should be vertical distance.

c) Using hand-written calculations, determine the instantaneous rates of change on

either side of each intersection point, and show that the rates of change at each

intersection points do not differ by more than 10%. Use this equation for percent

change: (check the image uploaded)

All calculations of IROCs and percent change must be hand-written!