Question

In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.

Answer 1

We have to find the linear relationship for the cost of tuition in function of the year after 1990.

The cost in 1990 was $104, so we can represent this as the point (0, 104).

The cost in 1998 was $184, so the point is (8, 184).

We then can calculate the slope as:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(184-104)/(8-0) \\ m=(80)/(8) \\ m=10 \end{gathered}`

We can write the equation in slope-point form using the slope m = 10 and the point (0,104):

`\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}`

We can then write the cost c as:

`c=10x+104`

We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.

We can calculate it as:

`\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}`

Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:

`\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=(150)/(10) \\ x=15 \end{gathered}`

As x = 15, it correspond to year 1990+15 = 2005.

Answer:

a) c = 10x + 104

b) $224

c) year 2005.