An exchange rate of a currency is determined by the supply and demand of that currency. If there are greater demand for US currency, the value of that currency would increase. If the value of the US currency rate increase more than the UK, this means that there is more demand for the US currency than the UK currency. Higher interest rates in the US currency will also attract more investors to switch to the US banks, therefore the value of the US will also increase.
Higher exchange rate for a currency means the exchange rate becomes stronger. If interest rate in the US increases, global investors will get higher return from investing in the US, therefore the investment will increase. When the interest rate increases in the United States more than in the UK, the United States value currency will be greater than the UK, meaning the US currency will have more value than the UK.
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When the US exchange rates becomes higher than the UK, the exports from the US to the UK imports will decrease. The US exports will fall and imports will increase. This makes US exports into the UK more expensive so it may reduce UK imports. This may happen because the UK will not be able to pay for imports from the US at high rates, therefore the UK may decline the percentage of import from the US. When the exchange rate of the UK drops below the US exchange rates, buying goods from America will become more expensive. We all know it will then become cheaper for the US to buy goods from the UK, therefore the UK exports will become relatively more and more competitive which leads to the quantity of exports in the UK