Answer
$R = 46~\Omega$
Work Step by Step
We can find $R$:
$i = i_0~e^{-tR/L}$
$\frac{i}{i_0} =e^{-tR/L}$
$e^{tR/L} = \frac{i_0}{i}$
$\frac{t~R}{L} = ln(\frac{i_0}{i})$
$R = \frac{L}{t}~ln(\frac{i_0}{i})$
$R = (\frac{10~H}{1.0~s})~ln(\frac{1.0~A}{0.010~A})$
$R = (\frac{10~H}{1.0~s})~ln(100)$
$R = 46~\Omega$
