免费指数衰减计算器
计算指数衰减模型中随时间变化的剩余量。
%
剩余
590.49
Lost409.51
Pct Remaining59.05 %
Half Life6.58
公式
## Exponential Decay ### Formula **Remaining = Initial × (1 - r)^t** where r is the decay rate per period and t is the number of periods. ### Half-Life The time for the quantity to reduce to half: **t½ = ln(0.5) / ln(1 - r)**
计算示例
1000 decaying at 10% per period for 5 periods.
- 01Remaining = 1000 × (0.90)^5
- 02= 1000 × 0.59049
- 03= 590.49
- 04Amount lost = 409.51
- 05Half-life = ln(0.5)/ln(0.90) ≈ 6.58 periods
常见问题
What is exponential decay?
Exponential decay occurs when a quantity decreases by a constant percentage each period. Each period, a fixed fraction of the remaining amount is lost.
What is half-life?
Half-life is the time it takes for a quantity to reduce to 50% of its current value. After two half-lives, 25% remains; after three, 12.5%, etc.
What are real-world examples?
Radioactive decay, drug metabolism in the body, car depreciation, cooling of hot objects, sound decay in a room.
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