The percents of girts age x or younger who have been sexuaily active are given i

Question

The percents of girts age x or younger who have been sexuaily active are given in the table a. Create a logarithmic functon that models the data, using an Age Cumulative Percente input equal to the age of the girls b. Use the model to estimate the percent of girts age 18 or Active Girls 4 younger who have been sexualy active c. Find the quadratic function that is the best t tor the data ula d. Graph each of these functions on the same axes with the 16 17 18 19 27.8 43.9 62 5 3. data points to determine which function is the better model for the data a. Give the logarithmic function below Type integers or decimals rounded to the nearest thousandth as needed) b.The logarithmic model predicts that 1%ofgrts age 18oryor ger have been sexually active (Type an integer or decimal rounded to the nearest tenth as needed) ts c. Give the quadratic function below ssy- (Use integers or decimais for any numbers in the expression. Type integers or decimals rounded to the nearest thousandth as needed ) d. Which function is the better model for the data? O The logarithmic model is better Click to select your answer(s)

Explanation / Answer

Go to this link :
http://xuru.org/rt/LnR.asp

And enter in the coordinates thus :
(15,5.6)
(16,12.4)
(17,27.8)
(18,43.9)
(19,62.5)
(20,73.6)

And i get this function :
y = 250.655ln(x) - 678.588

-678.588 + 250.655ln(x) ----> ANS

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b)
Plug in x = 18 :
-678.588 + 250.655ln(18)
45.9% ----> ANS

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c)
Go to this link :
http://xuru.org/rt/PR.asp

And enter thus :
(15,5.6)
(16,12.4)
(17,27.8)
(18,43.9)
(19,62.5)
(20,73.6)

We get
0.613x^2 - 6.969x - 29.775 ----> ANS

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d)
Enter x = 18 :
43.233

which is better approximation than what we got for log function

So, quadratic is a better approximation

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