The infiltration capacity of a soil follows the Horton’s exponential model, $f=c_1+c_2e^{-kt}$. During an experiment, the initial infiltration capacity was observed to be $200$ mm/h. After a long time, the infiltration capacity was reduced $25$ mm/h. If the filtration capacity after $1$ hour was $90$ mm/h, the value of the decay rate constant, $k$ (in $h^{-1}$, up to two decimal places) is ________