Question

optional - ungraded ch 3 practice quizscore: 6/40 answered: 2/7question 3tuition costsin 1990, the cost of tuition at a large midwestern university was $102 per credit hour. in 2004, tuition had risen to $256 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.$c(x) = \boxed{}$in the year 2011, tuition will be $ \boxed{}$ per credit hour.in the year $\boxed{}$, tuition will be $399 per credit hour

Explanation:

Step1: Define linear function form

A linear function is $C(x) = mx + b$, where $m$ is the slope, $b$ is the y-intercept.

Step2: Identify given points

Let $x$ = years since 1990.

• 1990: $x=0$, $C(0)=102$, so $b=102$.
• 2004: $x=2004-1990=14$, $C(14)=256$.

Step3: Calculate slope $m$

Use slope formula $m=\frac{C(x_2)-C(x_1)}{x_2-x_1}$
$m=\frac{256-102}{14-0}=\frac{154}{14}=11$

Step4: Write linear function

Substitute $m=11$ and $b=102$ into $C(x)=mx+b$
$C(x)=11x + 102$

Step5: Calculate 2011 tuition

2011: $x=2011-1990=21$
$C(21)=11(21)+102=231+102=333$

Step6: Find year for $C(x)=399$

Set $11x+102=399$, solve for $x$:
$11x=399-102=297$
$x=\frac{297}{11}=27$
Year: $1990+27=2017$

Answer:

$C(x)=11x + 102$
In the year 2011, tuition will be $\$333$ per credit hour.
In the year 2017, tuition will be $\$399$ per credit hour.