Formulas relation to cities.
Infrastructure
Infrastructure is what gives a city its population. Before other factors are applied, the formula for population by infrastructure is:
Base Population = Infrastructure * 100
The cost of infrastructure increases exponentially per level, with a base price of $300. The formula for infrastructure cost is:
Cost Per Level = [((X-10)^2.2) / 710] + 300
Population Density Formula
The formula used for population density when factoring Disease is different than the actual population density. The reason for this, is that Disease (based on Population Density) will kill a percentage of the Base Population, lowering the displayed Population Density. If there was no difference, the formula would feed back on each other.
Population Density Formula for Equations
Population Density = Base_Population/Land_Area
OR
Population Density = Infrastructure*100/Land_Area
Displayed Population Density
PopulationDensity = Actual_Population/LandArea
Land Cost Formula
As in the case of Infrastructure, the cost of Land also increases in an exponential way. The formula for the cost of one unit of land is the following:
Land_Unit_Cost = 0.002*(Current_Land-20)^2 + 50
and, as a result, the formula used for the cost of newly purchased Land is:
New_Land_Cost = Land_Unit_Cost*New_Land
From the two above formulas, it is made evident that, since the price of new land depends on the level of your current land, it is more profitable to buy land in bulks. In other words, it is more profitable to get land from 500 to 1,000 than from 500 to 750 and then to 1,000.
However, there is one limitation: the game identifies several levels of land, meaning that they are bought in steps. The levels are 500, 1k, 1.5k, 2k land, etc. and each step is 500 Land (except for the first step which is 480, since your city gets 20 land when it is first built). This means that, if you decide to get for example from 20 to 1k land and buy that much land, the game will automatically calcualte two transactions instead of one: one from 20 Land to 500 and one from 500 to 1,000. The game calculates the optimized cost for the land you decide to purchase.
Keeping all of the above in mind, the following table results:
| Step | From | To | Cost ($) | Total ($) |
|---|---|---|---|---|
| 1 | 20 | 500 | 24,000 | 24,000 |
| 2 | 500 | 1,000 | 255,400 | 279,400 |
| 3 | 1,000 | 1,500 | 985,400 | 1,264,800 |
| 4 | 1,500 | 2,000 | 2,215,400 | 3,480,200 |
| 5 | 2,000 | 2,500 | 3,945,400 | 7,425,600 |
| 6 | 2,500 | 3,000 | 6,175,400 | 13,601,000 |
| 7 | 3,000 | 3,500 | 8,905,400 | 22,506,400 |
| 8 | 3,500 | 4,000 | 12,135,400 | 34,641,800 |
Note that the Tutorial will make you buy 500 Land at your first city and as such, your first city will have 520 Land at some point. Going to the next step and buying 480 Land to reach 1,000 will set you back to course of the optimized land purchases.
Basic Formula
Food production is affected by several factors, including farms, land area, radiation, and seasonal timing.
The basic formula for food production per turn in a city is:
Food Production = Farms * (Land Area / 500)
Modifiers to this basic formula include:
- If the Mass Irrigation Nation Project is built the formula is changed to Farms * (Land Area / 400)
- If the season is Summer the production is changed to Food * 1.2
- If the season is Winter the production is changed to Food * .8