If all other factors are held equal, a decrease in the interest rate should lead to a decline in the exchange rate. The reason for this is that changes in the interest rates that are offered to investors will also change the attractiveness of investments in the United States.
In general, when interest rates go up, in one country, investments in that country will yield a higher return to investors. People who loan money to firms, for example, will receive higher interest rates in return. (Of course, if inflation also rises, these higher interest rates will not be helpful to the investors.). When interest rates in the US drop, then, American investments will seem somewhat less attractive to foreign investors.
This will have an impact on foreign exchange rates. Exchange rates are, for the most part, set by supply and demand. When foreigners are less interest in buying American investments, they do not need to buy as many American dollars. When they are less interested in buying American dollars, demand for dollars drops. A decrease in demand means that, all other things being equal, the price of American dollars (the exchange rate) will drop as well.