To find:The number of students took at least one online college cource in 2012, using...

Concept: Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is Number of students $=0.0112x^2+0.4663x+1.513$
Using this model, we can approximate the number of students (in millions) taking at least one online college course between the period 2002 and 2012.
Here, x= 0 corresponds 2002
x= 1 corresponds 2003.
So, x= 12 corresponds 2012.
So, substituting x= 12 in the given model, we get the approximate number of students (in millions) who took at least one online college course in 2012.
So, Number of students in $2012=0.0112{\left(10\right)}^2+0.4663\left(10\right)+1.513$
= 0.0112(100) + 4.663 + 1.513
= 1.12 + 4.663 + 1.513
= 7.296 millions
Final statement:
Therefore, 7.296 million students took at least one online college course in 2012.