The cost function for a certain model of a digital camera given by $C = 12.00 x + 48,450$, where $C$ is the cost (in dollars) and $x$ is the number of cameras produced. Find the average cost per unit when $x = 100$. Round your answer to the nearest cent.
A) $\$ 49,650.00$
B) $\$ 484.50$
C) $\$ 12.00$
D) $\$ 496.50$
E) $\$ 484.62$

Question

Quizplus · Accepted Answer

The average cost per unit is given by the cost function divided by the number of units produced:

$$\frac{C}{x} = \frac{12.00 x + 48,450}{x} = 12.00 + \frac{48,450}{x}$$

Plugging in $x = 100$, we get:

$$\frac{C}{x} = 12.00 + \frac{48,450}{100} = 12.00 + 484.50 = 496.50$$

Rounding this to the nearest cent gives us $\$ 496.50$, which is choice D.

The Cost Function for a Certain Model of a Digital C=12.00x+48,450C = 12.00 x + 48,450C=12.00x+48,450

The Cost Function for a Certain Model of a Digital $C = 12.00 x + 48,450$