如何计算Exponential Growth

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Exponential growth and decay describe processes where the rate of change is proportional to the current value. Growth occurs when the rate is positive (population growth, compound interest, viral spread). Decay occurs when negative (radioactive decay, drug elimination, cooling). The continuous model uses the natural exponential function P(t) = P₀ × e^(rt).

公式

Growth: P(t) = P₀ × e^(rt), r > 0

P: P₀ × e^(−rt) — P₀ × e^(−rt)

分步指南

1Growth: P(t) = P₀ × e^(rt), r > 0
2Decay: P(t) = P₀ × e^(−rt), r > 0
3e is Euler's number ≈ 2.71828
4Doubling time (growth): t₂ = ln(2)/r ≈ 0.693/r
5Half-life (decay): t₁/₂ = ln(2)/r ≈ 0.693/r

例题解析

输入

P₀=1000, r=5%, t=10 (growth)

结果

P(10) = 1000 × e^(0.5) ≈ 1649

Doubling time = ln(2)/0.05 ≈ 13.9 years

输入

C-14 half-life 5730 yr, find % remaining after 10,000 yr

结果

≈ 29.8% remaining

常见问题

What is Exponential Growth?

How accurate is the Exponential Growth calculator?

The calculator uses the standard published formula for exponential growth. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Exponential Growth calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Exponential Growth calculator use?

The core formula is: Growth: P(t) = P₀ × e^(rt), r > 0. Each step in the calculation is shown so you can verify the result manually.

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