Assuming this is not a learning curve problem, which has different definition of the terms.
Improvement rate does not have a standardized definition.
In terms of rate as time/unit, then we define improvement rate as time required for the next unit divided by the time required for the current unit.
=> improvement rate, r = T_n+1 / T_n
If the context defines rate differently, please post the contextual definition.
Here we have
T_1=10, T_3=5.68
we arrive at the equation
T_3=T_1*r^2
solving for r, we have
r=sqrt(T_3/T_1)=sqrt(5.68/10)=0.7537
Or improvement rate is 0.7537