Black Death Algebra
Introduction
In July of 1360, the black plague hit Europe once again. The rate at which the plague spread was so fast that many towns lost a large proportion of their population.
There was not much that a town could do to save themselves once the plague arrived. However, if they heard that the plague had hit nearby regions, they could expect that it would arrive soon, and the early warning meant that the townspeople could prepare themselves by going into lockdown.
Since the plague had permeated Europe many times throughout the middle ages, a large amount of data was available regarding the arrival of the plague at different cities. Using these data, it is possible to calculate the rate at which the black plague spreads throughout the region.
There are many different variables that you can look at to measure the spread of the disease. For instance: * How long it takes for the plague to spread from one place to another * The time taken for the plague to spread throughout an area * How quickly the plague spreads throughout a population
The Task
Choose a set and complete the appropriate parts of this assignment booklet. Show all of your calculations.
For the Extended Response questions, you will need to explain your process, show all of your calculations, and give your answers as full sentences that refer back to the original question. Set | Parts | Consolidating | A & B | Advanced | A & C | *Challenge Question | *D |
Part A: Time taken between two points 1. The following information regarding the time taken for the plague to spread from one town to another was found in the record books: Town 1 | Town 2 | Time taken | Distance | Constanța, Romania | Bucharest, Romania | 74 days | | Hamburg, Germany | Kiel, Germany | 32 days | | Le Mans, France | Rennes, France | 51 days | | Bologna, Italy | Modena, Italy | 15 days | | Tarancón, Spain | Madrid, Spain | 27 days | |
a. Using Google maps, find the distance between these towns and enter it into the table. Note that the plague only spread where people went, so the distance between two towns will follow the roads between the towns, not the countryside. Note: If Google maps lists the distances in miles, to change the units to kilometres, click on Show Options and then click on km. b. Describe any relationship you notice between Distance from one town to the other and the Time taken for the plague to spread between the towns.
c. Using the pronumeral t to represent Time taken, and d to represent Distance, write an equation that approximates d in terms of t.
d. In your equation, what is the coefficient of t?
2. Three other cities had this data and wanted to use it to work out how many days they had before the plague arrived from neighbouring infected towns. Town | Neighbouring infected towns | Distances | Time predicted | Nuremberg, Germany | Ingolstadt | | | | Amberg | | | | Ansbach | | | Ashford, England | Hastings | | | | Dover | | | | Canterbury | | | Innsbruck, Austria | Bolzano | | | | Salzburg | | | | Telfs | | |
e. Using the information in Question 1, write an equation that expresses t in terms of d.
f. In your equation, what is the coefficient of d?
g. Find the distances between the cities using Google maps, and enter these data into the table. h. Substitute the distances (d) into your equation for Question 2a to predict the time it will take for the plague to spread between these cities, and enter this into the table.
Extended response: As it turned out, the plague didn't arrive in Innsbruck from Telfs for over a month. Look back at Google maps and suggest two reasons why the plague may have spread slower to this town.
Part B: Time taken through varied terrain 1. As the plague spread throughout Europe, more information about the rate at which the infection spread
