If real GDP doubled from year 1 to 2, which must be true?

While it is possible for prices to increase, the doubling of real GDP specifically indicates that output has increased, not necessarily that prices have changed in any specific manner. In fact, real GDP is adjusted for inflation, meaning that significant price increases would not affect the measure of real GDP itself.

The change in real GDP does not directly correlate with government spending. Real GDP can increase due to various factors, including consumer spending, investment, or exports, in addition to government spending. Therefore, it is incorrect to assert that government spending must have doubled.

The exchange rate pertains to the value of one currency in relation to another and is not inherently linked to real GDP changes. A doubling of real GDP does not imply any changes to exchange rates, as these are influenced by different economic factors including trade balances and monetary policy.