The First Update of Epoch Four

Exponential decay shrinks the learning rate by multiplying it by a fixed factor $\gamma$ slightly below 1, over and over. After the multiplication has been applied $k$ times, the rate is

$$\alpha = \alpha_0\,\gamma^{k}$$

A teammate's training script contains this loop:

• train_set holds 1,620 examples.
• batches(...) walks through them 64 at a time and keeps the smaller final batch made of whatever is left over. Every batch, full or not, gets one call to update_weights.

The teammate's notes describe the schedule as "exponential decay from 0.1, $\gamma = 0.98$, 2% smaller each epoch."

According to the code as written, what learning rate does the very first update of epoch 4 use?

Give your answer rounded to 5 decimal places.