Question

the scatterplot shows data on the percentage, p, of 18 - to 24 - year - olds enrolled in degree - granting institutions over the past several decades, where t stands for years since 1965. a line of best fit is shown on the graph. what does the p - intercept of the model tell us about the enrollment of 18 - to 24 - year - olds in degree - granting institutions?
choose 1 answer:
a about 22% of 18 - to 24 - year - olds were enrolled in a degree - granting institution in 1965.
b the number of 18 - to 24 - year - olds enrolled in a degree - granting institution increased by 0.4% each year from 1965 to 2010.
c the percent of 18 - to 24 - year - olds enrolled in degree granting institutions increased by 18% from 1965 to 2010.
d the percent of 18 - to 24 - year - olds enrolled in degree granting institutions increased by 22% from 1965 to 2010.

Explanation:

The \( P \)-intercept of a linear model \( P = mt + b \) occurs when \( t = 0 \). Here, \( t \) represents years since 1965, so \( t = 0 \) corresponds to 1965. The \( P \)-intercept is the value of \( P \) (percentage of 18 - 24 - year - olds enrolled) when \( t = 0 \). Option A states that about 22% of 18 - to 24 - year - olds were enrolled in a degree - granting institution in 1965, which matches the interpretation of the \( P \)-intercept. Option B describes the slope (rate of change per year), not the intercept. Option C and D describe the total percentage increase over a period, not the intercept.

Answer:

A. About 22% of 18 - to 24 - year - olds were enrolled in a degree - granting institution in 1965.