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## Resources

Modeling Scenario

## 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

## Abstract

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.

## Citation

Researchers should cite this work as follows:

## 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.

## Authors

Author(s): Rachel Bayless1, Rachelle DeCoste2

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