Answer
The light intensity that emerges from the last filter is $~~0.33~I_0$
Work Step by Step
When unpolarized light passes through a polarizing filter, the intensity of the transmitted light is $0.5~I_0$ where $I_0$ is the original intensity. Thus the intensity is $I_1 = 0.5~I_0$ after passing through the first filter.
We can find the intensity $I_7$ after passing through the remaining six polarizing filters:
$I_7 = I_1~(cos^2~\theta)^6$
$I_7 = I_1~cos^{12}~\theta$
$I_7 = 0.5~I_0~cos^{12}~15^{\circ}$
$I_7 = 0.33~I_0$
The light intensity that emerges from the last filter is $~~0.33~I_0$
