The number of years, N(r), since two independently evolving languages split off from a common ancestral language is approximated by N(r)=-5000 In (r), where r is the percent of words from the ancestral language common to both languages. Find N if r=80%

Question

anonymous · Answer

I know how to set it up. It should look like 
N(r)=-5000 In (.80)
Though I am not sure what In stands for because my homework doesn't tell me. There is an example that my homework gave me if you would like me to write it down really fast and I can't figure out where they got their answer.

perl · Answer

ln stands for the natural logarithm

anonymous · Answer

oh! what is the natural log?

perl · Answer

ln(1) means the same as $\large  \log_e(1) $

perl · Answer

It is the logarithm with a base of a special constant $\large  e = 2.71818...$

anonymous · Answer

$$
e^{\ln x} = x \
\ln(e^x) = x\
\ln(x)  = \log_e(x)
$$

anonymous · Answer

Though $e^{\ln(x)}$ requires that $x>0$.

anonymous · Answer

oh ok! so it should be N(r)=-5000(2.718181)(.80)

perl · Answer

$ \Large  N(r)=-5000 \log_e (r)$

That decimal e=2.71828... never ends so its easier to just label it as e

anonymous · Answer

how do I type that into the calculator? I have a TI-84 C

perl · Answer

since r is a percent you want r / 100
80% = .80
$ \Large  N(.80)=-5000 \log_e (.80)$

There should be an LN button on your calculator

perl · Answer

-5000 ln(.80)

anonymous · Answer

I know you press 2nd then the LN button but I don't know what to type in there after I press those buttons

perl · Answer

you don't need to press 2nd LN

anonymous · Answer

Oh I got it thanks!

perl · Answer

2nd LN is e^x , a different function

anonymous · Answer

so the answer should be 1115.7178 and when we round it to the nearest whole number it should be 1116 right?

anonymous · Answer

is that right?

perl · Answer

yes

anonymous · Answer

awesome, thank you for your help!