The cost C (in dollars) of producing x units of a product is given by $C = 3.6 \sqrt { x } + 500$ . Find the additional cost when the production increases from 9 t o10.
A) $\$ 0.58$
B) $\$ 0.36$
C) $\$ 0.62$
D) $\$ 0.12$
E) $\$ 0.64$

Question

Quizplus · Accepted Answer

The additional cost is found by calculating the difference in cost between producing 10 units and 9 units. For 10 units: $C = 3.6\sqrt{10} + 500$, and for 9 units: $C = 3.6\sqrt{9} + 500$. The difference is $3.6\sqrt{10} - 3.6\sqrt{9}$, which simplifies to $3.6(\sqrt{10} - 3)$. Numerically, this equals approximately $0.58, hence the correct answer is A.

The Cost C (In Dollars) of Producing X Units of a Product