In this project I am going to examine the time taken for a whole tray of tomatoes to go bad when a single bad tomato is put in a particular position.

Authors Avatar

Contents Page

Introduction                 Page 3

Part 1                        Pages 4 to 7

Part 2                        Pages 8 to 16

Conclusion                Page 17

Introduction:

        In this project I am going to examine the time taken for a whole tray of tomatoes to go bad when a single bad tomato is put in a particular position.

        I will see how this time changes when I vary the size of the tray and alter the starting position. I will start with a small tray and gradually the size of the tray will be larger and also the positions will move from corner to corner, side to side and so on. At the end of this project I want to be able to have a formula which will tell me how long it would take a bad tomato to spread over cover the whole tray when the first bad tomato is placed in a curtain position in the tray.

Part 1

        The diagram below represents the look of a tray with 16 tomatoes in it. The number 1 is there to show where the first bad tomato began. The other numbers 2,3,4,5 and 6 represent the number of hours that have gone. Therefore for example after two hours in the diagram below in total, which includes the 1 and all the 2s, 4 tomatoes have gone bad.

Join now!

The table on the previous page tells me what is involved in the nth term. The column labelled ‘1st Difference’ tells us the difference between the number of bad tomatoes in the first hour to the second hour and so on. The column labelled ‘2nd Difference’ is the difference between the figures in the ‘1st Difference’ column. When the differences become the same this is when I can stop. If there was a ‘2nd Difference’ column then that means there will be a 2 involved in the nth term.  

        In total there are only 3 starting positions. They are one in the corner, one next ...

This is a preview of the whole essay