| linear | polynom | expon | log | trig | sat hyperb |
sigmoid | |
| shape of curve | straight | ||||||
| can X = 0? | yes | no | |||||
| can Y = 0? | yes | yes | |||||
| are either x or y undefined | no | ||||||
| units | any | none | degrees radians time |
||||
| range of useful values | any | x > 0 | x and y >0 | x and y >0 |
key features and salient information
| equation type | example | features & salient info |
image |
| linear | global grain production | LITE 13-17 pg 284 | |
| polynomial | none | related to area | |
| constant slope/ exponential |
natural capital degradation | increasing steepness related to population (i.e. growth) |
LITE 3-28 pg 74 |
| log | pH Stommel Q10 |
reaction rate large range of scale reaction rate vs. temp |
LITE 2-5 pg 36 EofN pg 13 EofN 2.25 pg 41 |
| trig | temperature over a year rainfall vs. season
|
seasonal or daily variation | LITE 5-14 EofN 4.9 pg 80 |
| sat hyperbola | limited sheep growth | approaching limit with time | LITE 8-4 pg 164 |
| sigmoidal | N fixation | slow start at low concentrations or populations | LITE 3-30 pg 76 |
| normal distribution | niche overlap | tolerance or proportion of diverse population | LITE 4-7 pg 91 |
| pulse | amount of fuel reserves | dynamic, not a statistical snapshot, changes over time or distance | LITE 15-16 |