Question 1190721: In 2014, TTEC had the following rate schedule for electricity usage for residential purposes;
Monthly service charge $200.00 Per KWh charge:
1st 600 KWh: $1.25/KWh
Over 600 KWh: $2.51/KWh
(i) What is the charge for using 599 KWh in a month?
(ii) What is the charge for using 2600 KWh in a month?
(iii) If C is the monthly charge for x KWh, develop a model relating the monthly charge and kilowatt-hours used. That is, express C as a function of x.
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's the breakdown of the electricity charges and the function relating monthly charge (C) to kilowatt-hours used (x):
**(i) Charge for using 599 kWh:**
* Since 599 kWh is less than or equal to 600 kWh, the rate is $1.25/kWh.
* Usage charge: 599 kWh * $1.25/kWh = $748.75
* Total charge: $748.75 + $200.00 (monthly service charge) = $948.75
**(ii) Charge for using 2600 kWh:**
* The first 600 kWh are charged at $1.25/kWh.
* Charge for the first 600 kWh: 600 kWh * $1.25/kWh = $750.00
* The remaining kWh (2600 - 600 = 2000) are charged at $2.51/kWh.
* Charge for the remaining 2000 kWh: 2000 kWh * $2.51/kWh = $5020.00
* Total usage charge: $750.00 + $5020.00 = $5770.00
* Total charge: $5770.00 + $200.00 (monthly service charge) = $5970.00
**(iii) Model relating monthly charge (C) and kilowatt-hours used (x):**
The monthly charge (C) as a function of kilowatt-hours used (x) can be expressed as a piecewise function:
C(x) =
* $200 + 1.25x, if x ≤ 600
* $200 + 1.25(600) + 2.51(x - 600), if x > 600
Simplifying the second part of the function:
C(x) =
* $200 + 1.25x, if x ≤ 600
* $200 + 750 + 2.51x - 1506, if x > 600
* $200 + 1.25x, if x ≤ 600
* $2.51x - 556, if x > 600
|
|
|
