Question 7: Consider the RMSProp optimizer update rule: v_t = \beta v…

Consider the RMSProp optimizer update rule:

$v_t = \beta v_{t-1} + (1 - \beta)(\nabla w_t)^2$

The algorithm runs for 10 iterations ($t = 0, 1, 2, \ldots, 9$).

After 10 iterations, what multiplicative weight is applied to the very first gradient term $(\nabla w_0)^2$ in the accumulated history $v_9$?

Assume $v_{-1} = 0$ and $\beta = 0.9$.

Enter the answer correct up to 3 decimal places.