Chapter 11.6, Problem 59E

To determine

Find the portion of the words from the ancestral language expect to occur in both languages today.

Answer to Problem 59E

  $70\%$ .

Explanation of Solution

Given information:

If two languages have evolved separately from a common ancestral language, the number of years since the split $n\left(r\right)$ , is modeled by the formula $n\left(r\right)=-5000\ln r$ , where $r$ is the percent of the words from the ancestral language that are common to both languages now If two languages split off from a common ancestral language about 1800 years ago.

Calculation:

Consider the given equation,

  $n\left(r\right)=-5000\ln r$

  $r$ is the percent of the words from the ancestral language

  $\begin{array}{l}\ln r=\left(\frac{n\left(r\right)}{-5000}\right)\\ r=e^{\left(\frac{n\left(r\right)}{-5000}\right)}\\ putn\left(r\right)=1800\\ r=e^{\left(\frac{1800}{-5000}\right)}\\ r=e^{\left(\frac{18}{-50}\right)}\\ r=0.7\\ r=70\%\end{array}$