A typical monthly utility rate / Current and resistance

[johann1301h]

Homework Statement

A typical monthly utility rate structure might go something like this: $1.60 for the first 16 kWh, 7.05 cents/kWh for the next 34 kWh used, 5.02 cents/kWh for the next 50 kWh, 3.25 cents/kWh for the next 100 kWh, 2.95 cents/kWh for the next 200 kWh, 2.35 cents/kWh for all in excess of 400 kWh. Based on these rates, what would be the charge for 327 kWh?

The Attempt at a Solution

Here are a few guesses how I think it should be solved
- Take the average between 2.35 cents/kWh and 2.95 cents/kWh.
- Find a function that "fits" these data and use that function for 327 kWh.

 

[phinds]

Homework Statement

A typical monthly utility rate structure might go something like this: $1.60 for the first 16 kWh, 7.05 cents/kWh for the next 34 kWh used, 5.02 cents/kWh for the next 50 kWh, 3.25 cents/kWh for the next 100 kWh, 2.95 cents/kWh for the next 200 kWh, 2.35 cents/kWh for all in excess of 400 kWh. Based on these rates, what would be the charge for 327 kWh?

The Attempt at a Solution

Here are a few guesses how I think it should be solved
- Take the average between 2.35 cents/kWh and 2.95 cents/kWh.
- Find a function that "fits" these data and use that function for 327 kWh.

Why would you feel the need for an approximation when the math to get the exact answer is so utterly trivial?

 

[johann1301h]

Is it? I don't see it as trivial...

 

[johann1301h]

Is there an obvious exact answer?

 

[David Lewis]

Where do current and resistance (in the title of your OP) come into play?

 

[johann1301h]

P = V^2/R
P = I^2*R
P = I*V

 

[David Lewis]

Power, voltage, resistance and current are not mentioned in the problem statement.

 

[johann1301h]

The problem is given in a chapter called Current and resistance

 

[phinds]

Is there an obvious exact answer?

yes

 

[johann1301h]

I have tried seeing a pattern in the numbers;

16 34 50 100 200 400

but I can't see one

 

[willem2]

I have tried seeing a pattern in the numbers;

16 34 50 100 200 400

but I can't see one

There's no need for guessing here. There's just a straightforward computation. Suppose the bill was for 50 kwh. The first 10 cost $1.60, so 40 kwh remain, The next 34 cost 7.05, so that's 34x7.05. and 6 kwh remain. The next 50 cost 5.02/kwh, but there is only 6 left to pay for. Compute 1.60+34*7.05+6*5.02 and you're done.

 

[johann1301h]

Thanks, this was way simpler than I thought!