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Modeling Scenario

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1-032-WordPropagation-ModelingScenario

Author(s): Rachel Bayless1, Rachelle DeCoste2

1. Agnes Scott College, Decatur GA USA 2. Wheaton College, Norton MA USA

Keywords: Google exponential growth language word problems etymology Ngram propagation Jumbo

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Abstract

Resource Image This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn

Description

How do you quantify a word's popularity?

Suppose you have a sentence consisting of 10 words, and the word jumbo appears exactly once. On the other hand, suppose you have a paragraph consisting of 100 words, and the word jumbo appears exactly once. Does this example change your definition of popularity?

We want popularity to be a function of time. Let us define t to be years. The word jumbo first appeared in print in 1861; thus our function will only be defined for t > 1861. Then define popularity as a function of time t by

P(t) = Percentage of words published in books in year t that is the word jumbo.

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Authors

Author(s): Rachel Bayless1, Rachelle DeCoste2

1. Agnes Scott College, Decatur GA USA 2. Wheaton College, Norton MA USA

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