Final answer:
The statement that a decline in the exchange rate means it would cost less USD to buy one euro is false. A decline in the exchange rate actually results in needing more USD to purchase one euro, indicating a depreciation of the dollar relative to the euro.
Step-by-step explanation:
A decline in the exchange rate means that the value of one currency decreases relative to another. So, if the exchange rate between the US dollar and the euro falls, it actually means that it costs more USD to buy one euro, not less. Therefore, the statement that a decline in the exchange rate means that it would cost less USD to buy one euro is false.
For example, if the exchange rate goes from 1 euro being worth 1.2 USD to 1 euro being worth 1.5 USD, it now costs more dollars to buy the same amount of euros. The decline in the value of the dollar compared to the euro could be attributed to various economic factors such as changes in interest rates. If U.S. interest rates decline compared to the rest of the world, there would likely be a decrease in demand for dollars and an increase in supply of dollars, leading to the depreciation of the dollar compared to other currencies such as the euro.