Exponential Growth Calculator
A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.
Result
A at t = 10
1,648.7213
Doubling time: 13.86 units.
- FormulaA₀ · e^(kt)
- Multiplier1.6487
- Doubling time (rule of 72)14.40
- Growth ratio per t=11.0513
Step-by-step
- Continuous: A = 1000 × e^(0.05 × 10) = 1000 × e^0.5 = 1000 × 1.6487 = 1,648.7213.
How to use this calculator
- Enter initial value, growth rate, and elapsed time.
- Pick continuous or discrete compounding.
- Read the value at time t.
About this calculator
Exponential growth: a quantity that grows at a rate proportional to its current size. Continuous form (e^kt) for processes with constant per-unit-time growth rate; discrete form ((1+r)^t) for periodic compounding. The doubling time follows from solving 2 = e^kt or 2 = (1+r)^t.
Frequently asked
Doubling time ≈ 72 / (rate %). A 6% growth rate doubles in ~12 years. It's an approximation of the exact ln(2)/k formula.
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