A chemist is studying the properties of a bronze alloy (mixture) of copper and tin. She begins with $6$ kg of an alloy that is one-half tin. Keeping the amount of copper constant, she adds small amounts of tin to the alloy. Letting $x$ be the total amount of tin added, define $$C(x)= \mbox{Concentration of tin} \ = \frac{\mbox{Total amount of tin}}{\mbox{Total amount of alloy}}.$$

(a) Find a formula for $\ C(x) =$ .

(b) Evaluate $\ C(0.5)=$ .

(c) Evaluate $\ C(-0.5) =$ .

(d) On a separate piece of paper graph $y= C(x)$, labeling all interesting features.

(e) Based on your graph give values where each of the following features occur and enter the letter of the statement below which best explains the physical significance of that feature.

A  As you continue to increase the amount of tin added, the alloy will eventually have a concentration of nearly 100%.
B  This is the initial number of kg of tin in the alloy.
C  This is the initial concentration of the alloy.
D  This is the maximum number of kg of tin you can remove from the alloy.
E  There is no such feature on the graph, so this has no physical meaning.

There is a horizontal asymptote at $y =$ which means .

There is a zero at $x =$ which means .

There is a $y$-intercept at $y =$ which means .