Suppose that I did a geometric average of the sequential significance and linear significance functions. That way, neither terribly dominates the other at all time points, preventing the former from being motivationally significant up to some *t** and thereafter the latter being motivationally significant. (Threshold of motivational significance.) (This addresses concerns that at some point the former's curve intersects the latter's and for *t* thereafter lies lower than it.)

Here's a graph of each of these functions, considered:

Data used for this graph, as generated from the following equations:

t | Linear | Sequential | Geom Avg |
---|---|---|---|

1 | 0.1 | 0.5 | 0.2236067977 |

2 | 0.2 | 0.6666666667 | 0.3651483717 |

3 | 0.3 | 0.75 | 0.474341649 |

4 | 0.4 | 0.8 | 0.5656854249 |

5 | 0.5 | 0.8333333333 | 0.6454972244 |

6 | 0.6 | 0.8571428571 | 0.7171371656 |

7 | 0.7 | 0.875 | 0.7826237921 |

8 | 0.8 | 0.8888888889 | 0.8432740427 |

9 | 0.9 | 0.9 | 0.9 |

10 | 1 | 1 | 1 |

Linear: `t/10`

Sequential: `t/(1+t)`

Geom Avg: `SQRT( Linear * Sequential )`

BLAH I realized that I've framed the above in terms of totals, not marginals. This theory zooms in on marginal changes, yet I've presented them in the roundabout form of totals.