A certain machine, which had an original value of $10,000 when

Question

A certain machine, which had an original value of $10,000 when purchased new, depreciated in value each year for 9 years. For each year after the machine was purchased, its value was at most 80 percent of its value the previous year. What was the maximum possible value, in thousands of dollars, of the machine 9 years after it was purchased?

A. $(10*0.8)^8$
B. $(10*0.8)^9$
C. $10(0.8)^8$
D. $10(0.8)^9$
E. $10(0.8)^{10}$

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Official Answer

D

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Bunuel · Answer

To find the maximum possible value, let’s assume the value of the machine was exactly 80% of its value from the previous year, not less. Then, its value in 9 years would be $10,000 * 0.8^9. However, note that the question asks for the value  in thousands of dollars . Therefore, expressed in thousands of dollars, the value is 10 * 0.8^9.

Answer: D.

pakman95 · Answer

I am not getting the expressed in thousands of dollars piece.

How is 10,000 * .8^9 = 10(.8)^9?

JUNGWOO1023 · Answer

In thousands of dollars means in $000 form acctually. You can think ignore 3 zero

Riyaagoell · Answer

I dont understand the difference between the options B and D

Bunuel · Answer

Brackets matter.

In option B, (10*0.8)^9 means the entire product 10*0.8 is raised to the 9th power, which is (8)^9.

In option D, 10(0.8)^9 means only 0.8 is raised to the 9th power, then multiplied by 10: 10 * (0.8^9).

So:
 
 B = (8)^9 
 D = 10 * (0.8^9)

bot00078 · Answer

Year  
  What happens to the Value (V)  
  Calculation  
 
   0  
 Original Value 
 10000 $ 
 
   1  
 $V0 * 0.8 (80 Percent) 
 $10000 * 0.8 
 
   2  
 $V1 * 0.8 (80 Percent)  
 $10000 * 0.8 * 0.8 
 
   9  
 $V8 * 0.8 (80 Percent)  
 $10000 * 0.8 (9 times)

So by this way we grab the ans as 10(0.8)^9
Here if you think B can be ans but its not becasue be is telling including (10000 * 0.8) ^ 9 which is wrong becasue we are not taking 10000 always we take the new value come after every year from the 80 percent calculation

I HOPE ITS HELP

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Year	What happens to the Value (V)	Calculation
0	Original Value	10000 $
1	$V0 * 0.8 (80 Percent)	$10000 * 0.8
2	$V1 * 0.8 (80 Percent)	$10000 * 0.8 * 0.8
9	$V8 * 0.8 (80 Percent)	$10000 * 0.8 (9 times)

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