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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%

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  1. anonymous
    • one year ago
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    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
    • one year ago
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    ln stands for the natural logarithm

  3. anonymous
    • one year ago
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    oh! what is the natural log?

  4. perl
    • one year ago
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    ln(1) means the same as \(\large \log_e(1) \)

  5. perl
    • one year ago
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    It is the logarithm with a base of a special constant \(\large e = 2.71818...\)

  6. anonymous
    • one year ago
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    \[ e^{\ln x} = x \\ \ln(e^x) = x\\ \ln(x) = \log_e(x) \]

  7. anonymous
    • one year ago
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    Though \(e^{\ln(x)}\) requires that \(x>0\).

  8. anonymous
    • one year ago
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    oh ok! so it should be N(r)=-5000(2.718181)(.80)

  9. perl
    • one year ago
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    \( \Large N(r)=-5000 \log_e (r)\) That decimal e=2.71828... never ends so its easier to just label it as e

  10. anonymous
    • one year ago
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    how do I type that into the calculator? I have a TI-84 C

  11. perl
    • one year ago
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    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
    • one year ago
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    -5000 ln(.80)

  13. anonymous
    • one year ago
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    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
    • one year ago
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    you don't need to press 2nd LN

  15. anonymous
    • one year ago
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    Oh I got it thanks!

  16. perl
    • one year ago
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    2nd LN is e^x , a different function

  17. anonymous
    • one year ago
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    so the answer should be 1115.7178 and when we round it to the nearest whole number it should be 1116 right?

  18. anonymous
    • one year ago
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    is that right?

  19. perl
    • one year ago
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    yes

  20. anonymous
    • one year ago
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    awesome, thank you for your help!

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