ABC Electric Company charges its customers in dollars per the number of kilowatt hours (kWh) of electricity used each month during the Winter-Spring months of November - June. The piecewise function C(x) below is the function used to calculate the cost, C in dollars, of a customer's electric bill for using x kilowatt hours.

C(x) = 12 + 0.143x if 0x100

26.30 + 0.116(x100) if 100< x500

72.74 + 0.108(x500) if x >500

a) Roughly sketch the graph of C(x). Label the points at x= 0, 100. ,and 500. Label the x axis y axis, and the tick marks. Briefly explain the scale you use for the axes, for example does each tick mark represent 1 unit or 20 units? Why did you pick that scale?

b) Find the monthly charge for a customer who used 350 kWh. Clearly show your arithmetic.

Which part of C(x) did you use and why?

c) Using the context of the problem, interpret the first line in the piecewise function:

12 + 0.143x if 0x100

In other words, what does 12 represent and what does 0.143x mean?