By California law, electric utilities should charge more per energy unit as customer's energy use rises, to give customers financial incentive to conserve energy use is divided into tiers, expressed as the percent of baseline usage, with higher prices for every higher tier of use. PG&E's present residential electric rates, expressed in dollars per kilowatt-hour for every tier of use are given below.

tier 1 up to baseline usage $0.12233 per kWh
tier 2 over 100% up to 130% of baseline $0.13907 per kWh
tier 3 over 130% up to 200% of baseline $0.29276 per kWh
tier 4 over 200% up to 300% of baseline $0.33276 per kWh
tier 5 over 300% of baseline usage $0.49051 per kWh

a) Make thetable of electric bills for different amounts of electricity used by the customer with baseline usage of 300 kWh per month
b) State electric bill as the single piecewise function of usage
c) Draw and label the graph of electric bill as the function of usage
d) Determine amount of electricity which produces the bill of $40
e) Create another column in the table for average cost per kWh as it depends on amount of electricity used.
f) Explain pattern you observe in average cost per kWh. Explain how that pattern is associated to pricing rule.