Highway to Hell

By: Amrita Kumar & Mihir Kapadia

The Starting Stages

Before even starting to create our rollercoaster, we knew we would have difficulties with the rational, exponential and logarithm functions as they each have restrictions. Understanding this, our knowledge from our Advanced Functions class, and previous math classes, guided us through the process of creating our rollercoaster on Desmos.

We first tried to use 'base functions' with minimal transformations to make the rollercoaster simple and smooth, however that did not work for all of the functions because they would either go past the maximum height or they wouldn’t reach it. We wanted to touch the maximum height at least one time in the duration of the ride, so in order to determine the formulas for all of our functions, we generally took the end point of one function and substituted it into the next function to see where the point of intersection would be. In addition, we modified the transformations accordingly so that the rollercoaster would not go past the maximum or minimum height.

A difficulty we came across was in terms of how our drafted rollercoaster physically differed from our final rollercoaster. We found that we could not always find the exact intersection point between two functions, unless we wanted to go into many decimal places, and that our final rollercoaster was not as 'smooth' as it would realistically be.

Functions & General Descriptions

Solving at 250 ft.

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Solving at 12 ft.

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Average Rate of Change from 10 to 15 Seconds

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Average Rate of Change from 50 to 60 seconds

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Instantaneous Rate of Change at 35 Seconds

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