Question 1190384
The question is asking about how long the *average* viewer will continue to watch the show.  Since viewership is declining at a constant *percentage* rate each month, this is an exponential decay situation.  The average time a viewer continues to watch is related to the reciprocal of the decay rate.

Here's how to think about it:

* **Decay Rate:** 30% per month, or 0.30 as a decimal.

* **Average Viewing Duration:** The average time a viewer continues to watch the show is the inverse of the decay rate.

Average Viewing Duration = 1 / Decay Rate

Average Viewing Duration = 1 / 0.30

Average Viewing Duration = 3.33 months (approximately)

So, the average viewer will continue to watch the show for approximately 3.33 months.