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 \(={0.0112}{x}^{2}+{0.4663}{x}+{1.513}\)

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.

Calculation:

The given model is Number of students \(={0.0112}{x}^{2}+{0.4663}{x}+{1.513}\)

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.