Answered

Find the best solutions to your problems with the help of IDNLearn.com. Find accurate and detailed answers to your questions from our experienced and dedicated community members.

In 1990, the cost of tuition at a large Midwestern university was $94 per credit hour. In 2004, tuition had risen to $290 per credit hour.
Determine a linear function
C
(
x
)
to represent the cost of tuition as a function of
x
, the number of years since 1990.

Sagot :

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.

To learn more about Linear Functions, click on the link below.

https://brainly.com/question/21107621

#SPJ9

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.