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Flip to reveal answersWhat is depreciation in terms of a geometric sequence?
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All 8 Flashcards — Depreciation
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Question
What is depreciation in terms of a geometric sequence?
Answer
Compound decay — a value loses a fixed percentage each year, multiplying by r = 1 − rate (0 < r < 1).
Question
A depreciation question asks 'after how many whole years is it first worth less than $X?'. Method?
Answer
Set PV × rⁿ < X with r = 1 − rate, then solve for n (logs or the GDC table) and round UP to the next whole year. It is 'first below', so you need the smallest whole n.
Question
A car worth $24 000 loses 12%/yr. Value after 5 years?
Answer
24 000 × 0.88⁵ ≈ $12 666.
Question
A model is V = V₀ × bᵗ. What is the depreciation rate?
Answer
1 − b as a percent. E.g. V = 5000(0.92)ᵗ loses 8% a year.
Question
How is depreciation different from compound growth?
Answer
Growth multiplies by 1 + rate (> 1); depreciation multiplies by 1 − rate (< 1).
Question
Why doesn't a depreciating value reach zero?
Answer
It keeps a fixed percentage each year, so it shrinks geometrically but never actually hits 0.
Question
V = 18 000(0.9)ᵗ — what does the 0.9 mean?
Answer
The yearly multiplier: 90% is kept, so 10% is lost each year.
Question
Find the value of a $2000 laptop after 2 years at 30% depreciation.
Answer
2000 × 0.7² = 2000 × 0.49 = $980.
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Topic 1.4 hub
Financial applications
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Math AA SL exam skills
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