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Equation for Electricity Bill in One Month

A household electricity bill for one month in which 2,494 kWh (kilowatt per
hour) were used includes, among other charges, a distribution charge. The
bill reads:

Current Charges
Charges for - UTILITIES
Residential Rate: RS for Jun 9 - Jul 12
Distribution Charge:

Customer Charge 6.47
200 KWH at 1.79600000¢ per KWH 3.59
600 KWH at 1.59400000¢ per KWH 9.56
1,694 KWH at 1.47200000¢ per KWH 24.94

Transmission Charge:
2,494 KWH at 0.37700000¢ per KWH 9.40
Transition Charge:
200 KWH at 1.79800000¢ per KWH 3.60
600 KWH at 1.59400000¢ per KWH 9.56
1,694 KWH at 1.47300000¢ per KWH 24.95

Generation Charge:
Capacity and Energy
200 KWH at 4.82600000¢ per KWH 9.65
600 KWH at 4.23800000¢ per KWH 25.43
1,694 KWH at 3.88600000¢ per KWH 65.83
PA Tax Adjustment Surcharge at 0.11818100% 0.23

Total UTILITIES Charges $193.21
Pay This Amount No Later Than Aug 2, 2002 $193.21
Account Balance $193.21

a.Give the total distribution charge when electricity consumption is
(i) 150 kWh, (ii) 755 kWh, (iii) 920 kWh.

b. Describe the function that the utility company uses to find the total
distribution charge.

c. Sketch and describe the graph of the function.

d. Give the rate of change of the distribution charge if the electricity
consumed changes from 150 to 160 kWh.

e. Give the rate of change of the distribution charge if the electricity
consumed changes from 195 to 205 kWh.

f. Give the rate of change of the distribution charge if the electricity
consumed changes from 300 to 310 kWh.

Solution Preview

The cost for electricity is broken up into tiers. The rate per kWH changes depending on how much electricity the person used.

You can see that the total cost (in cents) comes from the following:

Customer Charge + Transmission Charge + Transition Charge + Generation Charge

Then, on top of this there is a PA Tax Adjustment Surcharge of 0.118181%, so you need to multiply the sum of charges by 1.00118181 to account for this:

Total Charge = (Customer Charge + Transmission Charge + Transition Charge + Generation Charge)*1.00118181

To write the function, we need to look at the different intervals for the number of KWH used:

For x < 200 KWH
Total cost in cents = (647 + 1.796*x + 0.377*x + 1.798*x + 4.826*x)(1.00118181)

For 200 < x < 800, we need to add the total for the customer charge, the total for x = 200 and the amounts for x above 200 KWH:

(647 + 1.796*200 + 0.377*200 + 1.798*200 + 4.826*200)(1.00118181)+
(1.594*(x - 200) + 0.377*(x - 200) + 1.594*(x - 200) + 4.238*(x - 200))(1.00118181)

For x > 800, we need to add the total for the customer charge, the total for x = 200, the total for x = 800 and the amounts for x above 800 KWH:

(647 + 1.796*200 + 0.377*200 + 1.798*200 + 4.826*200)(1.00118181)+ (1.594*600 + 0.377*600 + 1.594*600+ 4.238*600)(1.00118181) +
(1.472*(x - 800) + 0.377*(x - 800) + 1.473*(x - ...

Solution Summary

Equations for electricity bills in one month are examined.

$2.19