math problem help?

[lordsmurf]

A student wants me to check his answer. I have no clue.

A company believes it can reduce the cost of producing a product by 20 percent each time volume doubles. The cost to produce the first unit was $1,000. What would be the approximate cost of the 4,096th unit?

So what's the formula, and what's the answer?

Thanks.

[träskmannen]

My take on it would be this:
The doubling of the volume follows this series: 1,2,4,8,16,32,64,128,256,512,1024,2048,4096. It has doubled 12 times.

The cost of the first unit is $1000.
The cost of the second is $800 (volume has doubled, 20% reduction =0.8 *1000).
The cost of the fourth is $640 (volume has doubled again, 20% reduction of cost of the second = 0,8*800 = 0,8*0,8*1000 = 0.8 ^2 (squared)*1000
The cost after doubling the volume the third time is then 0.8*0.8*0.8*1000 =0.8^3*1000
The cost after doubling the volume n times = 0.8 ^n * 1000.

The cost of the 4096th unit (12th time the volume doubled) is 0.8^12 * 1000 = $68,7 (rounded to one decimal)


...or did I miss it completely?

[lordsmurf]

I've passed that along to him. Thanks TRASK!

[lordsmurf]

He didn't actually need help. He had an ulterior motive.

I sent this to a few people just to see who would attempt it and who would just roll their eyes at it. You took an unexpected route and outsourced it. But that's the American way!

Now even I'm personally guilty of sending "American jobs" overseas!

Thanks TRASK!

[träskmannen]

That was an interesting motive from the student - I like it!