2/1)]/(2 – 1). Although we haven't pursued this, the reader may wish to investigate what effect the inclusion of this condition in Solver may have on best-fit values. 2/1)]/(2 – 1). Although we haven't pursued this, the reader may wish to investigate what effect the inclusion of this condition in Solver may have on best-fit values.
For three cases of interest, a) 1 < 2, as in our case studied above, then after a sufficiently large time, Eq. (3) reduces to ![<i>N</i><sub>2</sub> = <i>N</i><sub>10</sub>[exp(–<i>lambda</i><sub>1</sub><i>t</i>)]<i>lambda</i><sub>1</sub>/(<i>lambda</i><sub>2</sub> – <i>lambda</i><sub>1</sub>) = <i>N</i><sub>1</sub>/[(<i>lambda</i><sub>2</sub>/<i>lambda</i><sub>1</sub>) – 1].](345_1m8.gif)
2 = 21, b) 2 < 21, and c) 2 > 21, it follows from Eq. (9) that after a large time a) N2 = N1, b) N2 > N1, and c) N2 < N1, respectively. From this analysis we understand what conditions must be met for whether or not the population of N1 crosses below that of N2 for large times. In our case studied above, the best-fit values result in 2/1 = 1.85, so the model equations (less background terms) show a crossover. However, this ratio is so close to the threshold value of two that, combined with the different constant background terms, within the experimental and analytical uncertainties involved in such a complex situation, it is not obvious how the actual long-term data compare, even after background terms are subtracted. We suggest that readers may be interested in similar investigations, but for 2/1 much different from the threshold value of two.
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