Answer
$\text{(a)}\quad$ $\$59$
$\text{(b)}\quad$ $180$ miles
$\text{(c)}\quad$ $300$ miles
$\text{(d)}\quad$ $[0,\infty)$
Work Step by Step
Given $C(x)=0.35x+45$, we have:
$\text{(a)}\quad$ Substitute $x = 40$ to find the cost:
$\quad \quad C(40)=0.35(40)+45=59$ dollars.
$\text{(b)}\quad$ The cost is $\$108$ so substiteu $108$ to $C(x)$ then solve for $x$:
$\quad \quad \quad\begin{align*}
108&=0.35x+45\\
108-45&=0.35x\\
63&=0.35x\\
\frac{63}{0.35}&=x\\
180&=x
\end{align*}$,
Thus $x=180$ miles.
$\text{(c)}\quad$ Let $C(x)\le150$ to obtain:
$\begin{align*}
0.35x+45&\le150\\
0.35x&\le150-45\\
0.35x&\le105\\
x&\le\frac{105}{0.35}\\
x&\le300
\end{align*}$,
thus $x\le300$ or the maximum is $300$ miles.
$\text{(d)}\quad$ Sinec $x$ represents the number of miles driven, then its value should be $0$ or higher. Thus, the domain of C requires that $x\ge0$ or $[0,\infty)$
