Question

The number of classified documents has increased approximately linearly from 8.2 million documents in 2001 to 17.4 million documents in 2005. Let n be the number

of documents (in millions) labeled as classified in the year that is tyears since 2000. Find
an equation of a linear model to describe the data.

Answer 1

n -8.2 = 2.3(t -1)

Explanation:

You are given definitions for the variables t and n, along with two data points:

(t, n) = (1, 8.2) and (5, 17.4)

The slope of the line between these points is ...

m = (y2 -y1)/(x2 -x1)

m = (17.4 -8.2)/(5 -1) = 9.2/4 = 2.3

The equation can be written in point-slope form as ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

n -8.2 = 2.3(t -1) . . . . a linear model describing the data

______

Additional comment

If we eliminate the parentheses and add 8.2, we get the point-slope equation ...

n = 2.3t +5.9