数学
已验证计算器，公式透明
Exponential Decay Calculator.
Calculates the remaining quantity of a substance after a given time, based on its initial amount, decay rate, and elapsed time.
您的输入
工作原理
- 1
Enter the initial amount of the substance.
- 2
Enter the decay rate as a percentage per time unit.
- 3
Enter the elapsed time in the same time units.
- 4
The calculator computes the remaining amount using the exponential decay formula.
initial_amount * exp(-decay_rate/100 * time_elapsed)常见问题
What is exponential decay?
Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, following the formula A = A0 * e^(-kt).
How do I interpret the decay rate?
The decay rate is the percentage decrease per time unit. For example, a 5% decay rate means the quantity decreases by 5% of its current value each time unit.
Can I use this for half-life calculations?
Yes, you can find the half-life by setting the remaining amount to half the initial amount and solving for time, but this calculator directly computes the remaining amount for a given time.
结果
公式已检查估算仅供参考——重要决策请咨询专业人士。
工作原理
Calculates the remaining quantity of a substance after a given time, based on its initial amount, decay rate, and elapsed time.
- Enter the initial amount of the substance.
- Enter the decay rate as a percentage per time unit.
- Enter the elapsed time in the same time units.
- The calculator computes the remaining amount using the exponential decay formula.
公式
此计算器背后的数学公式，供您核对结果。
Exponential Decay Formula
A(t) is the amount after time t, A0 is the initial amount, k is the decay constant (rate/100), and e is Euler's number.
Example:
Input: A0 = 100, k = 0.05, t = 10
Calculation: 100 * e^(-0.05*10) = 100 * e^(-0.5)
Result: ≈ 60.65
实际应用场景
此计算在日常生活中的应用。
Radioactive Decay
Estimate the remaining mass of a radioactive isotope after a certain period.
Example: Carbon-14 dating
Drug Clearance
Model how a drug concentration decreases in the bloodstream over time.
Example: Determine dosage intervals
Depreciation
Calculate the value of an asset that depreciates at a constant percentage rate.
Example: Car value after 5 years
提示与常见错误
Tips
- Ensure the time units match the decay rate units (e.g., if rate is per year, time must be in years).
- For half-life, use the formula t_half = ln(2) / k, where k = rate/100.
- Use a small decay rate for long-term processes to avoid extremely small results.
- Check that the initial amount is positive; negative values are not physically meaningful.
Common Mistakes to Avoid
- Forgetting to convert the percentage decay rate to a decimal (divide by 100).
- Using the decay rate as a decimal directly without dividing by 100.
- Confusing decay rate with half-life; they are related but not the same.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.