**Description**

This programme is essentially about exponential functions. As an example of such a function, we examine radio carbon decay and how it may be used to date old samples of organic material. The progr...amme starts near Glastonbury on an archaeloogical dig uncovering ancient wooden roadways. A sample of a post is taken for dating using radio carbon decay techniques. The basic theory of radio-carbon dating is followed through completely. Firstly, there is the randomness of decays. This is explained by comparison with throwing a large number of dice. In fact the equation for radio-carbon decay is an exponential function. A computer plot produces a graph for this function, but it requires an x-scale from 0 to 10,000 to produce a reasonably looking exponential curve. There then follows the problem of using this curve to date the wood. Firstly we need to understand how radioactive carbon got into the wood originally. Secondly, we need to measure the radio-activity in the sample. Film of laboratories at Harwell and the British Museum show the basic process of counting decays. Finally, one is left with the problem of solving the function to determine the age of the wood sample. Two methods are described. Firstly besection, secondly, using logarithms. The problem of changing bases of logarithms is briefly explained in terms of x and y scaling. As an aside, the bisection method throws up a solution to a mathematical problem. This programme can stand by itself and should be understandable to a greater or lesser extent by anyone familair with basic mathematics. The only exceptional sequence requiring more detailed knowledge of M101 mathematics is the digression to the subject of exponentials with irrational powers which uses the concept of mathematical "nests". Particularly interesting features of the programme are the outside locations at Westhay, near Glastonbury, where the Cambridge University Archaeological Department are excavating ancient wooden trackways, the laboratory techniques at Harwell, and the model of radio-active decay using one hundred coloured dice.

Module code and title: | M101, Mathematics: a foundation course |
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Item code: | M101; 07; 1983 |

First transmission date: | 10-04-1983 |

Published: | 1983 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:25:00 |

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Producer: | Glan Thomas |

Contributors: | Mike Crampin; Bob Margolis |

Publisher: | BBC Open University |

Keyword(s): | Ancient roads; Glastonbury; Harwell Laboratories; British Museum Laboratories; Carbon 14; Radio-carbon decay; Westhay; Logarithms |

Master spool number: | HOU4220 |

Production number: | FOUM166L |

Videofinder number: | 2458 |

Available to public: | no |