Question

the bar graph shows the percentage of college freshmen in a certain country with an average grade of a in high school. the data displayed by the bar graph can be described by the mathematical model ( p = \frac{4x}{5} + 25 ), where ( x ) is the number of years after 1980 and ( p ) is the percentage of college freshmen who had an average grade of a in high school. a. according to the formula, in 2010, what percentage of college freshmen had an average grade of a in high school? does this underestimate or overestimate the percent displayed by the bar graph? by how much? select the correct choice below and fill in the corresponding answer box to complete your choice. \\( \bigcirc \\) a. the model underestimates the actual value by \\( \square \\)%. \\( \bigcirc \\) b. the model overestimates the actual value by \\( \square \\)%. (the bar graph includes years 1980 (28%), 1990 (30%), 2000 (44%), 2010 (46%), 2018 (55%) with corresponding percentages of college freshmen.)

Explanation:

Step1: Determine x for 2010

2010 is 2010 - 1980 = 30 years after 1980, so \( x = 30 \).

Step2: Calculate p using the formula

Substitute \( x = 30 \) into \( p=\frac{4x}{5}+25 \):
\( p=\frac{4\times30}{5}+25 \)
\( p = 24 + 25 = 49 \)

Step3: Compare with bar graph value (46%)

The model gives 49%, bar graph gives 46%. So the model overestimates.

Step4: Find the difference

\( 49 - 46 = 3 \)

Answer:

B. The model overestimates the actual value by 3%.