Question

An electricity company charges its customers a fixed base charge of $6 a month, plus 10 cents per kilowatt-hour (kWh) for the first 500 kWh, 11 cents per kWh for the next 500 kWh, and 15 cents for all additional kWh. Express the monthly cost E as a function of the amount x of electricity used.

Answer 1

`E(k)= \left[ \begin{array}{c} {6+0.10k\,\,if\,\,0\leq k \leq500} & 6+500*0.10+0.11(k-500)\,\,if\,\,500<k\leq1000& 6+500*0.10+500*0.11+0.15(k-1000)\,\,if\,\,k>1000\end{array}`

Explanation:

The cost function has 3 branches,

1. Consumptions less than 500
2. Consumptions less than 1000
3. consumptions above a 1000

So the first branch the consumer pays 6 dollars plus .10cents for any additional kWh (k)

In the second, they pay the same as the first up to 500kWh, and after that they pay 0.11 for the additional kWh above 500: (k-500) but bellow 1000

In the third branch, for consumptions above 1000, they pay the fix amount, plus .10 for the first 500 (
`500*0.10`) , .11 for the additional 500 (
`500*0.11`) , and finally 0.15 for consumptions above 1000:
`0.15(k-1000)`