Electrical resistance:The resistance R (in ohms) to the flow of electricity is related to...

Electrical resistance:The resistance R (in ohms) to the flow of electricity is related to the length of the wire and its gauge (diameter in fractions of an inch). For a certain wire with fixed length, this relationship can be modeled by the function, where R(d) represents the resistance in a wire with diameter d.

a. As the diameter of the wire increases, what happens to the resistance? Evaluate the function at R(0.05), R(0.25), and R(0.5) to verify.

b. If the resistance is increasing, is the diameter of the wire getting larger or smaller?

c. Graph the function using an appropriate scale. Judging from the graph, use mathematical notation to describe what happens to the resistance in the wire as the diameter gets larger and larger.