The question is hypothetical.
In the real world, things don't happen this way. The currencies and exchange rates have evolved over a period of time. These rates were initially pegged to Gold Reserves (as most countries had Gold to back currencies), which subsequently got changed to US Dollar reserve, and today is mostly market determined based on demand and supply.
So in a real sense, if there is a new piece of land that is not explored/inhabited, the first colonizers would use the currency of their origin. For example, Greenland--which is today part of Denmark--is following the Danish Krone. If sometime in future, they become a separate country, they would have an equivalent Danish Krone and other reserves. When the new currency gets created, they would peg the value of this against other currencies. Typically, the transition to the new currency would be staged, and during the first stage it would be directly in line to the Danish Krone with a fixed rate. You'd use this as the basis for deriving the rate for other currencies, and over a period of time, it will become free market linked.
So essentially in your case, if the Xland is self sufficient [does not import or export anything from/to the external world] then there would not be any exchange rate, as the self-supporting Xlanders would have no value for the USD that you are giving them--what would they do with it? Now, if they are buying something from the outside world and need to pay in USD, any they don't have any USD, they would have to sell something they produce to generate the USD. In an ideal situation, the value of goods imported compared to the value of goods exported would determine the exchange rate. However, in the real world, there would be various other considerations; for example, if Xland wanted to store more USD reserves to purchase something in the future. Some of these considerations may be reflected in the exchange rate, some may not.
Once trade is established, it determines how the country Government and Central Bank are regulating the rate. If the rate is fixed, then the government is giving a guarantee. Depending on how much trust Xland has with others, they may pursue trade at that rate, or they may not. Therefore, it can't be very off from reality. If it is off, then they have other ways to nudge other countries to accept the fixed rates. China, for example, follows a fixed rate.
In a managed float, the central bank would intervene if the fluctuations are large. In floating, it would be a pure function of supply and demand, which is directly linked to current trades and future trades.
