Exponential Decay Calculator
Solve x(t) = x₀(1 − r)ᵗ for the final value, initial value, decay rate or time.
Change the values and press Calculate to work out your own figures.
Exponential decay
Fill in three of x₀, decay rate, time and x(t); leave the fourth blank.
Show the working
- x(t) = x₀ × (1 − r)^t
- = 250 × 0.88^5 = 131.933
Exponential growth
Fill in three of x₀, rate, time and x(t); leave the fourth blank. A negative rate is decay.
Show the working
- x(t) = x₀ × (1 + r)^t
- = 100 × 1.07^20 = 386.9684
How to use it
Fill in three of x₀, decay rate, time and x(t); leave the fourth blank. Fill in three of x₀, rate, time and x(t); leave the fourth blank. A negative rate is decay.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
x(t) = x₀ × (1 − r)ᵗ
Decay rate
A 12% decay rate keeps 88% each period.
Questions
What is 250 after 5 periods of 12% decay?
131.933.
Formulas
x(t) = x₀ × (1 − r)ᵗ
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).