College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 8

Jan works as a sales person in the electronics division of a department store. He earns a base weekly salary plus a commission based on the retail price of the goods he has sold if he sells $x$ dollars worth of goods in a week, his earnings for that week are given by the function $E(x) = 400 + 0.03x$
a.) Find $E(200)$ and $E(15,000)$

$
\begin{equation}
\begin{aligned}
E(2000) &= 400 + 0.03(2000)\\
\\
&= \$ 460\\
\\
\\
E(15,000) &= 400 + 0.03(15,000)\\
\\
&= \$ 850
\end{aligned}
\end{equation}
$


b.) What do your answers in part(a) represent?
The answers in part(a) represent the total earnings of Jan in a week including his base weekly salary plus his commision.

c.) Find $E(0)$. What does this number represent?

$
\begin{equation}
\begin{aligned}
E(0) &= 400 + 0.03(0)\\
\\
&= \$ 400
\end{aligned}
\end{equation}
$

This number represent Jan's base weekly salary. It shows that he wasn't able to sell any goods during this week.

d.) From the formula for $E$. Determine what percentage did Jan earns on the goods that he sells.
It shows from the formula that Jan is earning $3\% (0.03 \times 100)$ on his commision based on the price of the goods that he is selling.