Answer :
The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].
As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.
We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".
To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as
[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].
Here, if we consider (x = 0) at 1990, c(x) = 94.
And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].
Thus, we can consider (x₁, y₁) as (0, 94).
Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,
We can consider as (x₂, y₂) as (14, 290).
Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,
[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].
Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is [tex][c(x) = 14x+94][/tex].
- Linear Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output, and when a function can be depicted in form of a linear equation, it is known as a linear function.
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