A chemist is studying the properties of a bronze alloy of copper and tin. She begins with 2 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,


a) Find a formula for \(C(x)\)
b) Evaluate \( C(0.5) \) and \( c(-0.5) \). Explain the physical significance of these quantities.
c) Graph \( y=C(x) \)

5th Ed: #31

a) \( C(x) = \frac{1+x}{2+x} \), \( x \geq -1\)
b) \( C(0.5) = \frac{1+.5}{2+.5}=\frac{3}{5} \), this is the percentage of tin in the alloy after adding 0.5 kg of tin. \( C(-0.5) = \frac{1-.5}{2-.5}=\frac{1}{3} \), this is the percentage of tin in the alloy after removing 0.5 kg of tin.
c)