Starting from a trade balance, if the world interest rate falls, then, holding other factors constant, in a small open economy the amount of domestic investment will and net exports will .

domestic investment will increase and net exports will decrease .

Explanation:

Previously in trade balance, If world Interest falls : It becomes comparatively  lesser than relatively higher domestic interest rate. And makes domestic country a lucrative investment destination. This relatively higher domestic will lead to capital inflows & increase domestic investment.

When our currency is demanded more for capital inflows, its excess demand in foreign exchange market appreciates the currency & reduces exchange rate. At lower exchange rate & appreciated currency value, our exports become expensive & imports cheaper. This reduces exports & increases exports , hence reduces Net Exports.