Answer
The value of the dollar decreased by 12.4% over the first year.
Work Step by Step
We can find the value of $\$$1 in 2006:
$\$1 = \frac{1}{1.27}~Euro$
We can find the value of $\$$1 in 2007:
$\$1 = \frac{1}{1.45}~Euro$
Let $x$ be the decrease in the value of the dollar:
$\frac{1}{1.27}(1-x) = \frac{1}{1.45}$
$\frac{1}{1.27}~x = \frac{1}{1.27}- \frac{1}{1.45}$
$x = \frac{1.27}{1.27}- \frac{1.27}{1.45}$
$x = 0.124 = \frac{12.4}{100} = 12.4\%$
The value of the dollar decreased by 12.4% over the first year.
