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This is a basic algebra question, I could use a little assistant with I just want guidance with symbolic rule.

A photocopier was bought for 4000 dollars and depreciates at a rate of $500 per year.

Determine a symbolic rule for the value of the copier.

Here's what I have thought: $c$ represents the cost of the printer, $x$ represents the year.

$C=4000(x)-500$

Could this be a symbolic rule?

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  • $\begingroup$ Note what happens with the $x$ there! How much is it at year 1? Year 2? 3? Does that capture what the printer's value should be doing over time? $\endgroup$
    – Malice Vidrine
    Nov 7, 2013 at 0:27
  • $\begingroup$ Hint. If it is \$500 per year and $x$ the years past, then what is $500\,x$ represent? $\endgroup$
    – John Alexiou
    Nov 7, 2013 at 0:28
  • $\begingroup$ So this means that x is in the wrong place or should it be there at all? $\endgroup$
    – Theo
    Nov 7, 2013 at 0:36
  • $\begingroup$ The $x$ should be by whatever is different at different times. The \$4000 is always the same no matter what. No matter what year it is, you always payed \$4000. But we do know that something is changing over time... $\endgroup$
    – Malice Vidrine
    Nov 7, 2013 at 1:02

2 Answers 2

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Since the depreciation rate is constant, I suppose you understand that, as function of time, the value of the copier is linear. This means that Cost = a + b t (t being in years). At time t=0, the value Cost is 4000 (you just bought it), then a = 4000. After the first year (t=1), the cost is 4000 - 500 = 3500. Then a + b = 3500, then b = -500. So the value is just 4000 - 500 t.

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If $x$ is the number of years from the purchase, the value should be $$C=max\{4000-500x,0\}$$ The $max$ function is needed because the value cannot be negative, even after a long time.

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