Final answer:
The mathematical model predicts the number of students studying abroad based on the number of years since 1995. Extrapolation beyond the given timeframe (1981 to 2006) is unreliable. The 95 percent confidence interval calculation assists in understanding the proportion of U.S. teens intending to study abroad.
Step-by-step explanation:
The equation y=84,949(1.095)x represents a mathematical model that predicts the number of American students studying abroad with x corresponding to the number of years since 1995. To find the number of students studying abroad at a particular year after 1995, we substitute the value of x into the equation and solve for y. However, calculating the number of students studying abroad for any year before the dataset's range (1981 to 2006) through extrapolation is unreliable because the equation is derived from data within that range only.
For example, when x = 11 (which corresponds to 2006), we can substitute this value into the equation to calculate y. A similar approach is taken when conducting confidence interval calculations, such as finding the 95 percent confidence interval for the true proportion of U.S. teens, ages 15-19, who are planning to go to college in another country based on survey results. In this case, the sample proportion is given by 6% from a sample of 720 teenagers.