When Does the Effective Step Peak?

A model is trained with an exponentially decaying learning rate

$\alpha(t) = 0.6\,e^{-t/4}$

where the epoch $t \ge 0$ is treated as a continuous variable. Over the same run the gradient magnitude happens to grow linearly:

$\lVert \nabla L(t) \rVert = t$

The effective step size — how far the weights actually move at epoch $t$ — is the product of the two:

$s(t) = \alpha(t)\,\lVert \nabla L(t) \rVert$

At which epoch is $s(t)$ largest, and what is that largest value (to 3 decimal places)?