The percents of girls age x or younger who have been sexuall

The percents of girls age x or younger who have been sexually active are given in the table. a. Create a logarithmic function that models the data, using an input equal to the age of the girls. b. Use the model to estimate the percent of girls age 16 or younger who have been sexually active. c. Find the quadratic function that is the best fit for the data. d. Graph each of these functions on the same axes with the data points to determine which function is the better model for the data. a. Give the logarithmic function below. y = (Type integers or decimals rounded to the nearest thousandth as needed.) b. The logarithmic model predicts that % of girls age 16 or younger have been sexually active. c. Give the quadratic function below. y = (Use integers or decimals 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? The quadratic model is better. The logarithmic model is better.

Solution

I entered this into xuru.org --> regression tools ---> log regression

I entered coordinates like this...
(15 , 5.6)
(16,12.8)
(17,27.6)
(18,43.8)
(19,62.9)
(20,73.1)

And got the result below...

y = 249.5019993 ln(x) - 675.2934832

y = -675.293 + 249.502ln(x) -----> ANSWER

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b)
Plug in x = 16 :

-675.293 + 249.502ln(16)

16.4734313762698984

16.5% ---> ANSWER

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c)
y = 0.575x^2 - 5.725x - 39.95

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d)
Quadratic is a better approximation