Question

question 20 (3 points)
the percents of girls age x or younger who have been sexually active are given in the table.

age	cumulative percent sexually active girls
16	12.8
17	27.2
18	44.1
19	62.1
20	73.3

the logarithmic function that models the data, is $y = -676.566 + 249.889 \ln(x)$, where $x$ is the age or younger and $y$ is the percent who have been sexually active. use the model to estimate the percent of girls age 18 or younger who have been sexually active.

• $16.1\\%$
• $16.7\\%$
• $45.7\\%$
• $45.8\\%$

Explanation:

Step1: Identify the value of x

We need to find the percent for girls age 18 or younger, so \( x = 18 \).

Step2: Substitute x into the logarithmic function

The function is \( y = -676.566 + 249.889\ln(x) \). Substitute \( x = 18 \):
First, calculate \( \ln(18) \). We know that \( \ln(18) \approx 2.8904 \).
Then, calculate \( 249.889\times\ln(18) \approx 249.889\times2.8904 \approx 249.889\times2.8904 \approx 722.35 \) (approximate calculation).
Next, calculate \( y = -676.566 + 722.35 \approx 45.784 \approx 45.8\% \).

Answer:

45.8% (the option with 45.8%)