Solve the problem.
-The number of years since two independently evolving languages split off from a common ancestral language is approximated by $N(r)=-5000 \ln r$, where $r$ is the percent of words from the ancestral language common to both languages now. Find $r$ if two languages split about 1530 years ago. Round to the nearest percent.
A) $74 \%$
B) $153 \%$
C) $7 \%$
D) $15 \%$

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:Substitute 1530 for $N$ in the given equation and solve for $r$.$$1530=-5000 \ln r$$$$\frac{1530}{-5000}=\ln r$$$$-0.306=\ln r$$$$r=e^{-0.306} \approx 0.735$$$$r \approx 0.735 \times 100 = 73.5 \approx 74 \%$$

Solve the Problem N(r)=−5000ln⁡rN(r)=-5000 \ln rN(r)=−5000lnr , Where rrr Is the Percent of Words from the Ancestral Language Common

Solve the Problem $N(r)=-5000 \ln r$ , Where $r$ Is the Percent of Words from the Ancestral Language Common