Final answer:
British net exports are likely to increase and the British exchange rate is likely to depreciate when the U.S. real interest rate rises relative to the British real interest rate.
Step-by-step explanation:
If the U.S. real interest rate rises relative to the British real interest rate, it is likely that British net exports will increase, because British goods would become relatively cheaper for foreigners as capital flows into the higher yielding U.S. savings instruments. This would also likely lead to a depreciation of the British exchange rate as the demand for British pounds increases from foreigners wanting to purchase British goods and the supply of pounds increases as Brits invest more in U.S. assets.
In other words, a higher interest rate in the U.S. makes U.S. financial assets more attractive, leading to an inflow of foreign financial capital, and consequently an appreciation of the U.S. dollar. At the same time, it makes British financial assets less attractive to both Brits (who now prefer U.S. assets) and to Americans (who now find it more profitable to invest at home). As a result, the British pound is likely to depreciate, making British exports cheaper and therefore more competitive internationally, which typically increases net exports.