Question

Standard electricity costs 12.366 cents per kWh for the first 500 kWh used in one month. The electric company also charges an $18.57 per month fee for billing, anti-litter, drainage, and transportation. Let the variable "x" be the number of kWh used in one month. Let "y" be the total bill for one month. What is the linear equation that models the monthly cost?

Answer 1

The linear equation that models the monthly cost is
`y = 18.57+0.12366\cdot x`, for
`0\,kWh \leq x \geq 500\,kWh`.

Explanation:

We notice that total fee is the sum of two components:

1) Fixed cost (
`C_(f)`) - Charge for billing, anti-litter, drainage and transportation.

2) Variable cost (
`C_(v)`) - Cost as a function of electricity consumption.

All costs are given in US dollars (USD). Mathematically, the formula is described below:

`C_(T) = C_(f)+C_(v)`

Where
`C_(T)` is the total cost, measured in USD.

Now, we expand the formula as follows:

`C_(T) = y`

`C_(f) = 18.57\,USD`

`C_(v) = \left(0.12366\,(USD)/(kWh) \right)\cdot x`, for
`0\,kWh \leq x \geq 500\,kWh`

Where:

`y` - Total bill for one month, measured in USD.

`x` - Quantity of kWh used in one month, measured in kilowatt-hours.

Then,

`y = 18.57+0.12366\cdot x`, for
`0\,kWh \leq x \geq 500\,kWh`.

The linear equation that models the monthly cost is
`y = 18.57+0.12366\cdot x`, for
`0\,kWh \leq x \geq 500\,kWh`.