Exponential Growth and Decay Calculator
Apply an entered constant growth or decay rate to an initial quantity. Compare periodic and continuous models, view a time curve and find doubling time or half-life.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert the percentage rate to a fraction. Periodic change uses (1+r) raised to elapsed periods; continuous change uses exp(rt). Logarithms give the time for a factor of two increase or decrease.
Periodic: y=y₀(1+r)^t; continuous: y=y₀e^(rt); characteristic time=ln(2)/|k|, with k=ln(1+r) or r
Worked example
Starting at 100 with periodic growth of 10% for 5 periods gives 161.051. Periodic decay of 50% for 3 periods gives 12.5 and a half-life of 1 period. Continuous 10% over 5 periods gives about 164.872127.
Assumptions and input details
Rates are entered assumptions and stay constant; this is a mathematical scenario, not a forecast or a biological, financial or radioactive-material assessment. A period can be any consistent time unit. Fractional periods use exponential interpolation. Periodic rates must be above −100%; continuous rates may be negative without that bound. The rate magnitude is limited to 1000%, elapsed time to 1e6 periods and computed quantities to 1e−100–1e100. Zero rate has no finite doubling time or half-life. No added amounts, capacity limit or varying rates are included.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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Enter two known points and a target x or y. Calculate the other coordinate, view the straight-line model and clearly distinguish interpolation from extrapolation.
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