4. This is how linguists use language to help determine the age of a civilizatio

Question

4. This is how linguists use language to help determine the age of a civilization:
* they make a list of basic words in the original language (house, man, etc.)
* they determine how many words are still in use
* they assume the rate at which words leave the list is proportional to the number of
words still in use from the list.
The basic list for classical Latin has 210 words with 144 still in use in modern Italian. Suppose the proportionality constant is k=.22 . Let t be measured in thousands of years. How long did it take modern Italian to develop?

Explanation / Answer

Y= words in use. dY/dt= -.22Y dy/y= -.22dt lny= -.22t +C y= Ce^(-.22t) C= 210 144= 210 e^(-.22t) e^(-.22t)= 144/210= 0.685714 -.22 t= ln(0.685714)= -0.377294 t= -0.377294/-.22= 1.715 thousand years.

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