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price of microchip

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by leugene » Thu Aug 28, 2008 12:06 pm
I think this is 2.

At the start, the price is $81. After 6 months, it will be 1/3 of its price, or $27. At one year, it will be 1/3 of that, or $9. At 1.5 years, it is $3. At 2 years, it is $1.

I believe two years is the right answer.
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by leugene » Thu Aug 28, 2008 12:20 pm
Algebraically, it is 1=[81][(1/9)^x], where 1 is the ending price, [81] is the starting price, (1/9) is the fraction of the starting price given x, where x is the amount of time in years. You can see the trend of how it declines after time goes on, and if you plug in for x, you will see that 2 is correct. Luckily, it doesn't take us until 10, 20, etc. to find the answer.
Last edited by leugene on Thu Aug 28, 2008 1:17 pm, edited 1 time in total.
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Re: price of microchip

by stern » Thu Aug 28, 2008 12:48 pm
ddm wrote:The price of microchip declines by 67% every 6 months.At this rate approx. how many years will it take for $81 microchip to reach to $1?

A.1.5
B.2
C.3
D.13
E.13.5
Decline of 67% ~ 1/3 the price

81/(3^4) = 1 => 4*6 months = 2 years.

IMO B.
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by ddm » Thu Aug 28, 2008 4:47 pm
OA-B
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