Problem 4: The number of years, N(r), since two independently evolving languages split off from a common ancestral language is approximated by N(r) = -5000 ln r where r is the proportion of words from the ancestral language that are common to both languages. Find the following:
a. Sketch the graph of N(r).
b. Find and interpret the value of N(0.5).
c. How many years have elapsed since the split if 70% of the words of the ancestral language are common to both languages today?
d. If two languages split off from a common ancestral language about 1000 years, find the proportion of the words that are common to both languages.