PHARM/PCS V5 · Procedure 24 Drug Decay and Binding
Exponential Growth and Decay
Fit a single exponential to time-course data and get the rate constant, the coefficient, and the half-life, each with confidence limits.
What it computes
Fits x = A·e−kt to (t, x) data by regressing ln(x) against t. Reports the rate constant k, the coefficient A, the half-life, and confidence limits on all three.
Inputs and outputs
You provide
- Time and value, one pair per line
- A confidence level
PHARM/PCS reports
- Rate constant k and coefficient A
- Half-life, with asymmetric confidence limits
- Confidence limits on the fitted line
- A plot of the data with the fitted exponential
When to use it
For any single-exponential process (drug elimination, radioactive decay, bacterial growth with positive k) where you want the rate constant and half-life. It's the general-purpose exponential tool that the specialized decay (Procedure 21) and pharmacokinetic procedures (26-32) specialize.
Reading the results
Log-transforming to linearize weights small values more heavily, so late-time points near the noise floor can tug the slope; watch for scatter widening at low x. A poor straight-line fit on the ln scale means the process isn't a single exponential; a two-phase decay needs the compartmental treatment in the PK procedures.
A half-life with limits, not just a number
The half-life carries confidence limits derived from the slope limits, the way the book does it. They come out asymmetric because a half-life is a reciprocal. A poor straight line on the log scale means the process is not a single exponential, and a two-phase decay needs the compartmental procedures instead.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.