Final Summative: Roller-Coaster Model

MHF 4U0 - Brian, Nicholas & Srushti


In the creation of our roller-coaster model, we incorporated thirteen different equations, which consisted of either a linear, quadratic, polynomial, rational, sinusoidal, exponential, and logarithmic function. The initial objective was to keep our roller-coaster fun, different, and most of all realistic. Our first step in creating our roller-coaster was placing the given maximum and minimum height, and also incorporating it in the given time of 100 seconds. Next, we added in the functions into the graphing calculator one by one. As we add each function, we discuss the appropriate transformations and restrictions where each function would be suitably fit. It was also important to make sure the requirements were met, such as have a function at the maximum height of 300 feet and a minimum height of 10 feet. As we arranged each function, we made sure that it was realistic in terms of utility and had no mathematical errors. In order to make the roller-coaster practical, we concluded that the roller-coaster would start at the minimum height of 10 feet then incline to the maximum height of 300 feet and finally end off at the minimum height. Throughout our process, we had one main difficultly which was, determining where each function would be placed, this was because each function had its own uniqueness which would benefit our design in numerous ways.

Description of Functions:

Height VS. Time

All Equations: (with restrictions)

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All Functions: (indicated on graph)

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1.) Solve for the exact time(s) when the rollercoaster reaches a height of:

a) 250 feet

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b) 12 feet
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2.) Calculate Average Rate of Change from:

a) 10 to 15 seconds

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b) 50 to 60 seconds
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3.) Calculate Instantaneous Rate of Change at:

a) 35 seconds
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Average Instantaneous Rate of Change:
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Roller-Coaster Simulation

Roller-Coaster Simulator

Rough Graphs & Parent Function Graphs: