The scatterplot shows data collected over time, and a regression curve is used to model the pattern.

Extrapolation means using a model to make predictions slightly outside the observed data range. In Applied Algebra, extrapolation can be appropriate when:

" the regression model fits the data reasonably well "

and the predicted x-values are not too far outside the observed data.

From the scatterplot, the data points appear to run approximately from:

x=3 " to " x=15

So the observed data range is about:

15-3=12

A reasonable extrapolation range extends a little beyond the data, but not too far. The interval:

x=0 " to " x=18

extends about 3 units beyond each side of the observed data, which is reasonable.

The interval:

x=-3 " to " x=21

extends much farther beyond the data and would be less reliable.

Also, r^2does not have to equal exactly 1 for extrapolation to be useful. A value less than 1 can still represent a strong model.

Therefore, the correct answer is:

▭ ( " A " )