## anonymous one year ago 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%

1. anonymous

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.

2. perl

ln stands for the natural logarithm

3. anonymous

oh! what is the natural log?

4. perl

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

5. perl

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. perl

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

10. anonymous

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

11. perl

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

12. perl

-5000 ln(.80)

13. anonymous

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

14. perl

you don't need to press 2nd LN

15. anonymous

Oh I got it thanks!

16. perl

2nd LN is e^x , a different function

17. anonymous

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

18. anonymous

is that right?

19. perl

yes

20. anonymous

awesome, thank you for your help!