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example 3 Residential Power Costs
Chapter 3.3
Excluding fuel adjustment costs and taxes, Georgia Power Company charges its residential power customers for electricity during the months of June through Septemberaccording to the table.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
b. Find C(950) and explain what it means.
c. Find the charge for using 1560 kWh in a month.
2009 PBLPathways
2009 PBLPathways
Excluding fuel adjustment costs and taxes, Georgia Power Company charges its residential power customers for electricity during the months of June through Septemberaccording to the table.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
b. Find C(950) and explain what it means.
c. Find the charge for using 1560 kWh in a month.
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If 0 to 650 are used:
$7.50 plus $0.04657 per kilowatt hour 7.50 0.04657x
1 7.50 0.04657 1
2 7.50 0.04657 2
3 7.50 0.04657 3
650 7.50 0.04657 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 650, up to 1000 used:
$37.77 plus $0.07738 per kWh above 650 37.77 0.07738 650x
651 37.77 0.07738 651 650
652 37.77 0.07738 652 650
653 37.77 0.07738 653 650
1000 37.77 0.07738 1000 650
x
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 1000 used:
$64.85 plus $0.07976 per kWh above 1000 64.85 0.07976 1000x
1001 64.85 0.07976 1001 1000
1002 64.85 0.07976 1002 1000
1003 64.85 0.07976 1003 1000
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 1000 used:
$64.85 plus $0.07976 per kWh above 1000 64.85 0.07976 1000x
1001 64.85 0.07976 1001 1000
1002 64.85 0.07976 1002 1000
1003 64.85 0.07976 1003 1000
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 1000 used:
$64.85 plus $0.07976 per kWh above 1000 64.85 0.07976 1000x
1001 64.85 0.07976 1001 1000
1002 64.85 0.07976 1002 1000
1003 64.85 0.07976 1003 1000
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 1000 used:
$64.85 plus $0.07976 per kWh above 1000 64.85 0.07976 1000x
1001 64.85 0.07976 1001 1000
1002 64.85 0.07976 1002 1000
1003 64.85 0.07976 1003 1000
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
If more than 1000 used:
$64.85 plus $0.07976 per kWh above 1000 64.85 0.07976 1000x
1001 64.85 0.07976 1001 1000
1002 64.85 0.07976 1002 1000
1003 64.85 0.07976 1003 1000
x
x
x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
a. Write the piecewise-defined function C that gives the monthly charge for residential electricity, with input x equal to the monthly number of kilowatt-hours.
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
b. Find C(950) and explain what it means.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(950) 37.77 0.07738(950 650)
60.984
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
b. Find C(950) and explain what it means.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(950) 37.77 0.07738(950 650)
60.984
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
b. Find C(950) and explain what it means.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(950) 37.77 0.07738(950 650)
60.984
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
c. Find the charge for using 1560 kWh in a month.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(1560) 64.85 0.07976(1560 1000)
116.694
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
c. Find the charge for using 1560 kWh in a month.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(1560) 64.85 0.07976(1560 1000)
109.5156
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
2009 PBLPathways
c. Find the charge for using 1560 kWh in a month.
Monthly Kilowatt-Hours (kWh) Monthly Charge
0 to 650 $7.50 plus $0.04657 per kWh
More than 650, up to 1000 $37.77 plus $0.07738 per kWh above 650
More than 1000 $64.85 plus $0.07976 per kWh above 1000
(1560) 64.85 0.07976(1560 1000)
109.5156
C
7.50 0.04657 if 0 650
( ) 37.77 0.07738 650 if 650 1000
64.85 0.07976 1000 if 1000
x x
C x x x
x x
