Fresh catalyst is loaded into a reactor before the start of the following catalytic reaction.
$$\textbf{A} \longrightarrow \textbf{products}$$
The catalyst gets deactivated over time. The instantaneous activity $a(t)$, at time $t$, is defined as the ratio of the rate of reaction $-r_A^{\prime}(t)\left(\mathrm{mol}\right.$. $\left.(\mathrm{g} \mathrm{cat})^{-1} \mathrm{hr}^{-1}\right)$ to the rate of reaction with fresh catalyst. Controlled experimental measurements led to an empirical correlation
$$-r_A^{\prime}(t)=-0.5 t+10$$
where $t$ is in hours. The activity of the catalyst at $t=10 \; \mathrm{hr}$ is______________(rounded off to one decimal place).