Answer
$
\dfrac{N}{N_{o}}=0.0749
$
Work Step by Step
The equation of the decay is
$$
N=N_{o} e^{-\lambda t}
$$
For 10 days, the number of hours is $240 \mathrm{h}.$ Hence, the term $\lambda t$ could be calculated by
$$\lambda t =\left(0.0108 \mathrm{h}^{-1}\right)(240 \mathrm{h})=2.592$$
Now, we can get the fraction os the sample that will remain by
$$
\dfrac{N}{N_{o}}=e^{-2.592}=\boxed{0.0749}
$$
