SOLUTION: A furniture store is closing out its business. Each week the owner lowers prices by 25%. After how many weeks will the sale price of a $500 item drop below $100?

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Question 394562: A furniture store is closing out its business. Each week the owner lowers prices by 25%. After how many weeks will the sale price of a $500 item drop below $100?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = # weeks
Then after w weeks , the price becomes 500%2A0.75%5Ew.
Then we want 100+%3C+500%2A%280.75%29%5Ew, or 0.20+%3C+0.75%5Ew.
If w = 5, 0.75%5E5+=+0.2373 to four decimal places.
If w = 6, 0.75%5E6+=+0.187 to 3 decimal places.
So AFTER 6 weeks, the price should be less than $100.
Though technically speaking it will only take ln0.2%2Fln0.75+=+5.59 weeks (or after 5 weeks and Thursday of the new week) for the price to be lower than $100.