Which of the following terms describes a decline in the value of the euro compared to the American dollar over time?

Appreciation is the opposite of depreciation; it refers to an increase in the value of a currency compared to another currency. If the euro appreciates against the dollar, it means that the euro has strengthened, making it more valuable relative to the dollar, which is not the case in the context of a decline in value.

Amortization pertains to the gradual repayment of a loan or the allocation of an intangible asset's cost over time. It does not relate to currency value or exchange rates. Thus, this term is irrelevant when discussing changes in the value of currencies such as the euro and the dollar.

Nominalization is a linguistic term that refers to the process of converting a verb or an adjective into a noun. This concept is unrelated to economic terms or currency valuation. Therefore, it does not apply to the discussion of the euro's decline in value against the dollar.