# 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.

Extracts from this document...

Introduction

## 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.

Middle

5

6

7

8

9

10

6

7

8

9

10

7

8

9

10

8

9

10

9

10

10

Now I am going to find out how many differences are involved.

Hours (n) | Total No. Of Bad Tomatoes | 1st Difference | 2nd Difference |

1 | 1 | ||

2 | |||

2 | 3 | 1 | |

3 | |||

3 | 6 | 1 | |

4 | |||

4 | 10 | 1 | |

5 | |||

5 | 15 | 1 | |

6 | |||

6 | 21 | 1 | |

7 | |||

7 | 28 | 1 | |

8 | |||

8 | 36 | 1 | |

9 | |||

9 | 45 | 1 | |

10 | |||

10 | 55 |

Now I know that there is a 2 involved in the formula as there are 2 differences. So I will now place the numbers in table to find out the formula. To begin with I will double the number and then 2 it. If that does not work I will try to use different ways such as 2ing and then misusing the n number.

N | n² | n²-n | n²+n | (n²+n) / 2 | T |

1 | 1 | 0 | 2 | 1 | 1 |

2 | 4 | 2 | 6 | 3 | 3 |

3 | 9 | 6 | 12 | 6 | 6 |

4 | 16 | 12 | 20 | 10 | 10 |

5 | 25 | 20 | 30 | 15 | 15 |

6 | 36 | 30 | 42 | 21 | 21 |

As it can be seen I found the formula in four steps and these steps I may use in other trays further in this project.

The nth term is:

n²+n

2

So by putting the numbers we know in the formula (hours) we can find out how many tomatoes go bad in particular number of hours in a 10x10 tray with the bad tomato starting in a corner.

Now I am going to look at another position on a 10 x 10 tray. The position I am going to look as is starting from the middle.

5 | ||||||||

5 | 4 | 5 | ||||||

5 | 4 | 3 | 4 | 5 | ||||

5 | 4 | 3 | 2 | 3 | 4 | 5 | ||

5 | 4 | 3 | 2 | 1 | 2 | 3 | 4 | 5 |

5 | 4 | 3 | 2 | 3 | 4 | 5 | ||

5 | 4 | 3 | 4 | 5 | ||||

5 | 4 | 5 | ||||||

5 |

Conclusion

I believe the main reason behind this investigation is to find out the a formula that by just knowing the size of the tray and exact position in the tray of the bad tomato will tell how long it will take for all the tomatoes to go bad.

Before I write down the formula I will tell you how I arrived at it. The formula will tell you how long it will take to make all the tomatoes in the tray go bad. Firstly the formula should involved the size of the tray e.g. 6 x 8 and also must involved the starting position of the first bad tomato. Now that I have explained what have got to be in the formula, well, here it is.

(a-x) + (b-y)

‘a’ and ‘b’ stand for the width and depth of the tray. ‘x’ and ‘y’ stand for the positioning of the first bad tomato. So, for example if we take a 8 x 6 tray with starting bad tomato at the position (4,4) the working to find how long it will take for the whole tray to go bad should look like:

(a-x) + (b-y)

(8-4) + (6-4)

## Answer: 6 hours

This student written piece of work is one of many that can be found in our GCSE Bad Tomatoes section.

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