Math Question (Basic)

[Rain Man]

Originally Posted by cdcox

P2=P1*e^(-kt) is the integrated form of the geometric model. Also called a first order model. I would also call it an exponential growth model.

In the third model, Z is the "maximum" population that the resources in the area would support. That model approaches Z asymptotically.

I always tell my students (we need to do population projections to build water and wastewater plants that have to have a useful life of up to 50 years) that population projections are black magic and to get someone else to do them.

I use the following in-class example. Rank the following cities in terms of their 1910 and 1960 populations, and describe the driving forces for the change in population over that time interval:

Providence, RI
Detroit, MI
Miami, FL

Interesting. I've never done a resource-constrained model, in part because no one ever thinks their resources are constrained. Well, almost no one. And honestly, I kind of agree. I think of it in terms of that bet those two professors made about the price of zinc or something, and the one who bet on lower future prices won - innovation will always beat limitations.

As one exception to my usual situation, I did a study to locate a facility in a resort town once, and they said to assume that population growth would stop in X years because they would be at their limit of developable space. After some arguing, I built it in, but I don't believe that for a second. The place was desirable, and densities will always increase in desirable area because people will build up if they can't find ground of their own. And governments won't stop it if they can get big fees out of it. I see the same thing in my neighborhood - some developer tore down three houses and put up two high rises that now have 75 or 80 units. Manhattan is an example of how growth limits really don't apply in the real world other than in extreme cases.

I agree with you that population projections can get blindsided by unexpected extrinsic factors on a local level if you're doing a 50-year projection. I've never done projections that far out, so I haven't really thought about it. I think in that case, though, you have to just assume historic rates of growth will continue (with some adjustments for things like urban growth patterns) and hope for the best.

As another war story related to extrinsic impacts, I was on a project a couple of years ago for a small rural county, and people were bashing some land planning firm for developing a population projection that seemed unfathomable to the locals - something like quadrupling over 50 years. I stayed out of the fight, but thought it was funny that the locals didn't take one thing into account. A large metro area had expanded to where the first suburbs were just spilling across this county's borders. Generally, once you start becoming a suburb, populations explode beyond all historic data. I think the land planning firm was probably right, but hey, they hire a competitor of mine for all their research so let them defend their own damned selves.