Question: Social Science The number of years, \(N(r)\), since two independently evolving languages split off from a common ancestral language is approximated by

where \(r\) is the proportion of the words from the ancestral language that is common to both languages now. Find each of the following.

1. \(N(.9)\)
2. \(N(.5)\)
3. \(N(.3)\)
4. How many years have elapsed since the split if \(70 \%\) of the words of the ancestral language are common to both languages today?
5. If two languages split off from a common ancestral language about 1000 years ago, find \(r\).

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