Question

45pts!!! pls who work!!!

Answer 1

For the CFL bulb, the cost at 0 hours will be
`\$4`, and
`\$20.10` at
`10,000` hours.

For the LED bulb, the cost at 0 hours will be
`\$8`, and
`\$17.80` at
`10,000` hours.

Explanation:

Step 1: Calculating the cost for 0 hours

At
`0` hours, the bulbs aren't at use, and so none of them are utilizing any energy.

The lack of the use of energy, means no money has to be paid for the energy.

Thus, at
`0` hours, both bulbs have a cost that is equal to their subsequent prices:

CFL bulb:
`\$4`

LED bulb:
`\$8`

Step 2: Calculating the cost for 10,000 hours

For the CFL bulb,
`0.023` kWh is used within an hour.

So within
`10,000` hours, the amount of energy will be:

`0.023* 10000\\\\=230~\text{kWh}`

`7` cents is charged for each kWh, so for
`230` kWh, the cost will be:

`7* 230\\\\=1610~\text{cents}`

`1` dollar equals to
`100` cents, so the cost found above in dollars will be:

`100~\text{cents}=1~\text{dollar}\\\\\text{Divide by 100 on both sides of the equation:}\\(100)/(100)~\text{cents}=(1)/(100)~\text{dollar}\\\\\text{Simplify:}\\1~\text{cents}=(1)/(100)~\text{dollar}\\\\\text{Multiply by 1610 on both sides:}\\1* 1610~\text{cents}=(1610)/(100)~\text{dollar}\\\\\text{Simplify:}\\1610~\text{cents}=16.1~\text{dollars}`

So, the total cost for the CFL bulb, along with its original price will be:

`4+16.1\\=20.1\\=\$20.10`

Similarly, for the LED bulb,
`0.014` kWh is used within an hour.

So, within
`10,000` hours, the amount of energy will be:

`0.014* 10000\\\\=140~\text{kWh}`

`7` cents is charged for each kWh, so for
`140` kWh, the cost will be:

`7* 140\\\\=980~\text{cents}`

The cost found in dollars will be:

`100~\text{cents}=1~\text{dollar}\\\\\text{Divide by 100 on both sides of the equation:}\\(100)/(100)~\text{cents}=(1)/(100)~\text{dollar}\\\\\text{Simplify:}\\1~\text{cents}=(1)/(100)~\text{dollar}\\\\\text{Multiply by 980 on both sides:}\\1* 980~\text{cents}=(980)/(100)~\text{dollar}\\\\\text{Simplify:}\\980~\text{cents}=9.8~\text{dollars}`

So, the total cost for the LED bulb, along with its original price will be:

`8+9.8\\=17.8\\=\$17.80`