Answer
a. $C(x) = 15.37 + 0.0821x$ $(0 \leq x \leq 800)$
b. see the graph below
c. $31.79$ dollars
d. $56.42$ dollars
e. $0.0821$
Work Step by Step
a. $C(x) = 15.37 + 0.0821x$ $(0 \leq x \leq 800)$
b. see the graph below
c.
$C(x) = 15.37 + 0.0821x$
$C(200) = 15.37 + 0.0821(200)$
$C(200) = 31.79$
The monthly charge using $200kW$ is $31.79$ dollars
d.
$C(x) = 15.37 + 0.0821x$
$C(500) = 15.37 + 0.0821(500)$
$C(500) = 56.42$ dollars
The monthly charge using $200kW$ is $56.42$ dollars
e.
From the graph below
$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{56.42 - 31.79}{500-200}$
$m = \frac{24.63}{300}$
$m = 0.0821$
