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Math • Exponential Growth Calculator

Exponential Growth Calculator

Model exponential growth or decay over time with discrete or continuous compounding, plus the doubling or half-life period.

Model Type
Final Amount N(t)
1628.89
Doubling / Half-life Period
14.21 periods
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Calculation Guide & Reference

Exponential Growth & Decay Mathematics

Exponential growth calculator models growth or decay over time with discrete or continuous compounding, plus doubling time or half-life.

Standardized Mathematical Formula
N(t) = N₀ × (1 + r)^t

Exponential growth (or decay, if r is negative) compounds a growth rate r over t time periods, starting from an initial value N₀. A continuous-compounding variant uses N₀ × e^(rt) instead.

Variables:
N₀:Initial value
r:Growth rate per period (as a decimal)
t:Number of time periods
How It Works (Step-by-Step)
  • 1Enter the initial value, growth rate, and number of time periods.
  • 2View the final amount and the doubling time (or half-life, if the rate is negative).
Real-World Numerical Example
5% Annual Growth Over 10 Years

A population of 1,000 grows at 5% per year (discrete compounding) for 10 years.

•Final amount: 1,000 × (1.05)¹⁰ = 1,628.89.
•Doubling time: ln(2) / ln(1.05) ≈ 14.21 periods.
Result: After 10 years, the population reaches about 1,628.89, and it would take about 14.21 years to double.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Discrete compounding applies growth once per period: N₀(1+r)^t. Continuous compounding applies growth constantly: N₀e^(rt). Continuous compounding always produces a slightly higher result for the same nominal rate.

Doubling time = ln(2) / ln(1+r) for discrete compounding, or ln(2) / r for continuous compounding — this is sometimes approximated by the "Rule of 70," which divides 70 by the percentage growth rate.

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