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605-655 (Medium)|   Math Related|         
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bhavyagmat
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­A small business has just invested in a new piece of equipment. 04 Oct 2025, 04:24
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With constant rate - the value can never be zero
Elite097
KarishmaB how can constant rate imply absolute value
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aspernaturcumque
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­A small business has just invested in a new piece of equipment. 30 Apr 2026, 08:29
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guddo
­A small business has just invested in a new piece of equipment. The business's accountant estimates that the value of the equipment will decrease over time at a constant rate. Based on this assumption, the accountant properly estimates the value of the equipment 3 years afterward to be $X, 6 years afterward to be $Y, and 8 years afterward to be, for the first time, $0.

Select values for X and for Y that are jointly consistent with the given information. Make only two selections, one in each column.

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assume constant amount decrease every year to be x .
so after 3 years gap (FROM YEAR 3 TO 6) , amount = X-3x = Y.
amount after 2 years gap ( FROM YEAR 6 TO 8) -> Y - 2x = 0.
solving, X/Y = 5/2 .
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­A small business has just invested in a new piece of equipment. 14 Jul 2026, 10:29
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How can we infer here it is constant amount and not constant rate ?
Scholar94

­While waiting for KarishmaB's response, changing at a constant rate implies changing at a contant amount and changing at a constant percentage rate implies an exponential growth rate. So for this question, a contant rate simply means a constant amount
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­A small business has just invested in a new piece of equipment. 15 Jul 2026, 04:28
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Hi anknown123,

Great question, and it's the exact thing that tripped up a few others in the thread. The key is the little phrase "8 years afterward to be, for the first time, $0." That word $0 is the whole clue.

Here's the difference between the two readings:

Constant amount (what the question means): the value drops by the same number of dollars every year - say $100 per year. Start at $800 and you get 700, 600, 500, ... , 100, and then exactly 0 at year 8. It lands right on zero.

Constant percentage: the value drops by the same fraction every year - say 10%. Start at $800 and you get 720, 648, 583.2, ... The number keeps shrinking but never actually reaches 0. It just gets closer and closer forever.

So the question is telling you the value does hit exactly $0 at a specific year. A percentage decrease can never do that. The only way to reach a clean $0 at year 8 is a fixed dollar drop each year - a constant amount. That's how you infer it, straight from the stem, without needing any depreciation background.

Quick test to feel it: take $100 and cut it by 10% each year:

- Year 1: 90
- Year 2: 81
- Year 3: 72.9
- ... keeps going, never 0

Now cut it by a fixed $20 each year: 100, 80, 60, 40, 20, 0. Reaches zero on schedule.

Once you read "constant rate" as a constant dollar amount, the rest falls out: the value line is straight, and the numbers 500 (year 3) and 200 (year 6) fit a $100-per-year drop that ends at $0 in year 8.

Answer: Column 1 (X) = 500; Column 2 (Y) = 200

anknown123
How can we infer here it is constant amount and not constant rate ?

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