Exponential Growth Calculator
Exponential Growth/Decay
Calculate A = A₀ × eʳᵗ or A = A₀ × (1+r)ᵗ
Find Growth Rate
Find the rate given initial value, final value, and time
Doubling Time / Half-Life
Calculate doubling time or half-life from a rate
Formula
A(t) = A₀eʳᵗ | Doubling: t = ln(2)/r | Half-life: t₁/₂ = ln(2)/|r| | Rule of 72: t ≈ 72/r%
Frequently Asked Questions
What is exponential growth?
Exponential growth occurs when a quantity increases at a rate proportional to its current value. The formula is A(t) = A₀eʳᵗ (continuous) or A(t) = A₀(1+r)ᵗ (discrete). Examples: population growth, compound interest, viral spread.
What is the Rule of 72?
The Rule of 72 is a quick estimate: doubling time ≈ 72 / growth rate (%). For example, at 8% growth, the doubling time is approximately 72/8 = 9 periods. It's most accurate for rates between 2% and 12%.
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