This is what the original guide says about Exploration
Exploring is the act of growing by simply exploring for land. To play as explorer means that you will not train any offensive army and solely train enough military to defend your land. This is a very easy and simple way to get to know the game but you will not get the thrills of attacking. It is also good if you will not be able to be very active in your playing.
Terrain is a resource that must be created by Exploration, at the cost of platimum and draftees. The game provides some terrain, platinum and draftees at startup so the player is able to both Construct on the Terrain and Explore for more Terrain right away.
The Terrain does not have a size, it has a unit count. The unit of Terrain is 1 "acre of barren land", and it takes 12 hours of game time to explore. There is no limit on how many acres you may explore at the same time. Once the 12 hours passed and the acre or acres arrived, the explored acres are going to increase the cost per unit of the next Exploration.
To illustrate, lets assume the initial cost for exploring 1 acre is 100 platinum and 40 draftee, and at the start the game gave you 1000 platinum and 400 draftees. Your existing infrastructure is creating 100 platinum and 40 draftees every hour, so you can keep adding new Exploration.
In the very first our your graph would look like this: 1__2__3__4__5__6__7__8__9_10_11_12 . . . . . . . . . . . 10 Then one hour later it would look like this: 1__2__3__4__5__6__7__8__9_10_11_12 . . . . . . . . . . 10 1 Then, in 10 hours it would look like this: 1__2__3__4__5__6__7__8__9_10_11_12 . 10 1 1 1 1 1 1 1 1 1 1
Once the 10 acres arrive your exploration cost increase to 110 platinum and 50 draftees - and one hour later, when the first 1-acre arrives the next Exploration increases to 111 platinum and 51 per acre.
Here's a table showing the current draftee cost thresholds. Explore one acre too much and the cost goes up to the next row.
Plat Cost Formula
The platinum cost per acre is determined by
MAX(0.6 * (LAND^1.299), 850)
where LAND is the size of the dominion when exploration begins.