The number of years, N(r), since two independently evolving languages split off from a common ancestral language is approximated by N(r)= -5000 1n r, where r is the proportion of the words from the ancestral language that is common to both languages now. Find each of the following.find n if r=88%
just plug and chug.
N(.88) = -5000 ln(.88) ≈ 639
To find n when r is equal to 88%, we can substitute the given value of r into the equation N(r) = -5000ln(r) and solve for n.
Given:
r = 88% = 0.88
Substitute the value of r into the equation:
N(r) = -5000ln(r)
N(0.88) = -5000ln(0.88)
Now, we can use a calculator to find the natural logarithm of 0.88.
Using a calculator:
ln(0.88) ≈ -0.127
Substitute the value of ln(0.88) back into the equation:
N(0.88) = -5000(-0.127)
Now, we can simplify the expression:
N(0.88) ≈ 635.7
Therefore, when r = 88%, the number of years, N(r), is approximately 635.7.
To find the value of n when r is 88%, we need to substitute the value of r into the equation N(r) = -5000 ln(r) and solve for n.
Given:
r = 88%
Substituting the value of r into the equation:
N(r) = -5000 ln(0.88)
Now, we can solve for n by evaluating the natural logarithm of 0.88 and multiplying it by -5000:
N(r) = -5000 ln(0.88)
N(r) ≈ -5000 (-0.127436)
N(r) ≈ 637.18
Therefore, when r is 88%, the number of years since the languages split off is approximately 637.18 years.