Question

a tutor charges c dollars for a session that lasts h hours. the cost includes a fixed amount for travel expenses. use the graph to create a table of values for h = 0, 0.5, 1, 1.5, and 2. describe the meaning of the rate of change in terms of the context.

Explanation:

Step1: Find the fixed - travel cost

When $h = 0$, from the graph, $C$ is the fixed - travel cost. Looking at the graph, when $h=0$, $C = 10$.

Step2: Find the rate of change (slope)

The rate of change (slope $m$) of a line passing through two points $(h_1,C_1)$ and $(h_2,C_2)$ is given by $m=\frac{C_2 - C_1}{h_2 - h_1}$. Let's take two points, say $(0,10)$ and $(2,70)$. Then $m=\frac{70 - 10}{2-0}=\frac{60}{2}=30$.

Step3: Create the cost - function

The cost function is $C=30h + 10$.

Step4: Create the table of values

$h$	$C$
$0.5$	$30\times0.5 + 10=15 + 10 = 25$
$1$	$30\times1+10 = 40$
$1.5$	$30\times1.5+10=45 + 10 = 55$
$2$	$30\times2+10 = 70$

The rate of change of 30 means that for each additional hour of tutoring, the cost of the tutoring session increases by 30 dollars.

Answer:

$h$	$C$
$0.5$	$25$
$1$	$40$
$1.5$	$55$
$2$	$70$

The rate of change of 30 means the cost increases by 30 dollars per additional hour of tutoring.