According to a $1999$ study by Starkey and Scarnecchia, the average weight $W($in kg$)$ at the age $t($in years$)$ of channel catfish in the Lower Yellowstone River can be modeled by

$W(t)=(3\mathrm{.}46293-3\mathrm{.}32173e^{-0\mathrm{.}03456t}{)}^{3\mathrm{.}4026}$

Find the rate at which the weight is changing at age $t=7.$

$($Use decimal notation. Give your answer to five decimal places.$)$

rate: $k\frac{g}{?}$ year