No change in interest rates, but a change in attitude?

As expected the Reserve Bank of Australia (RBA) left the cash rate at 2.5%.

Since 2011 the RBA have been steadily reducing interest rates (from 4.75% to the current 2.5%) because they saw that the Australian economy was not growing as fast as it had been. The RBA  was therefore able to try and stimulate the economy (try and get it to grow faster) while inflationary pressures were subdued.

In announcing this decision the RBA made one important point, and signalled another by what they did not say.

The RBA suggested that the current rate is likely to remain the same for some months. A 'period of stability' was foreseen, which means rates staying where they are. This is probably because they feel at 2.5% they are providing enough stimulus to the economy.

The thing they didn't say was that the exchange rate of the Australian $ is too high and should fall. They had been saying this consistently for over a year and absence of this comment suggests they think the Aus$ has fallen far enough.

The exchange rate affects the price of imports and exports. When the exchange rate falls it means the price of Australian exports falls abroad, leading to higher sales volume. However the price of imports rises and this will put upward pressure on inflation.

The graph shows how the exchange rate against the US$ since 2011.

 The Sydney Morning Herald reports the RBA decision here

Question

Why does the interest rate affect the exchange rate?