The number of years N(r) since two independently evolving...

The number of years N(r) since two independently evolving languages split off from a common ancestral language is approximated by N(r) = -5000 ln r where r is the proportion of the words from the ancestral language that are common to both languages now. a. N(0.9) = (Round to the nearest tens place.) b. N(0.5) = (Round to the nearest hundreds place.) c. N(0.1) = (Round to the nearest thousands place.) d. How many years have elapsed since the split if 60% of the words of the ancestral language are common to both languages today? years have elapsed since the split. (Round to the nearest hundreds place.) e. If two languages split off from a common ancestral language about 1000 years ago, find r. r = (Round to the nearest tenth as needed.)

Transcript

00:01 Okay, so in this problem, we have the equation n of r, which is negative 5 ,000 lnr, and n represents the number of years since two languages evolve from an ancestral language.

00:16 R is the proportion of words that are common to both languages that are from the ancestral language.

00:26 So part a asks us to find n of 0 .9.

00:29 So we just plug that into the calculator, negative 5 ,000 ln of .9, and we have to round to the nearest tens place.

00:37 So if you plug that in, you get 526 .803.

00:41 If you round it to nearest tens, which is tens, not tenth, that would round up to 530.

00:48 Okay, so 530 years.

00:50 If only 50 % of the two languages are common, of words from the two languages are common to the ancestral language, then you plug in 0 .5 for r and you get 3 ,465 but we are rounding to the 100s, so that rounds up to 3 ,500 years.

01:13 If only 10 % of words from two languages are common to the ancestral language, then plugging into the calculator, you get 11 ,512 .926, but you're rounding to 1 ,000's place, so that's 12 ,000, 11 ,500.

01:31 Rounds up to 12 ,000.

01:33 Part d, how many years have elapsed since the split, if 60 % of the words of the ancestral language are common to both languages.

01:42 So 60%, you should expect your answer to be somewhere between a and b since it's 0 .6, which is between 0 .5 and 0 .9.

01:53 So if you plug that into your calculator, the 0 .6, you get 2 ,554, which rounds up to the 100%.

02:01 Its place to 2 ,600 years, which makes sense.

02:04 That is between these two numbers.

02:08 Now, part e says, if two languages split off from a common ancestral language about a thousand years ago, find r.

02:16 So now we know that n is a thousand, and we're finding r.

02:22 So we're solving for r.

02:23 So you got 1 ,000 divided by negative 5 ,000.

02:33 1 ,000 divided by negative 5 ,000.

02:36 And you get negative 1 .5, i mean negative 1 over 5...

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