CALCULATOR
Continuous Exponential Decay from Supplied Rate and Time Calculator
Continuous Exponential Decay from Supplied Rate and Time. Example: Initial: 100 units, Decay rate: 0.1 1/time, Time: 5 time gives 60.6530659713 units. Supplied nonnegative decay constant and compatible abstract time unit; no half-life sources or maintained domain model. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Supplied nonnegative decay constant and compatible abstract time unit; no half-life sources or maintained domain model. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Constant proportional decrease solves y′=-decay rate y.
Accepted inputs: Initial: 0.001 to 1,000,000 units; Decay rate: 0 to 1 1/time; Time: 0 to 20 time.
Continuous Exponential Decay from Supplied Rate and Time
How the calculation works
value=initial exp(-decay rate×time)
Worked example
With initial 100 units, decay rate 0.1 1/time, time 5 time, continuous exponential decay from supplied rate and time is 60.65306597 units.
Assumptions and limits
Supplied nonnegative decay constant and compatible abstract time unit; no half-life sources or maintained domain model. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Constant proportional decrease solves y′=-decay rate y.