To determine how many weeks it will take for the total number of viewings to reach approximately 5,937,075, we need to look at the pattern of increase in the number of viewers each week.
We start with:
- Week 1: 150,000 viewers
Each week, the number of viewers increases by 20%. This makes the viewers in the following weeks:
- Week 2: 150,000 1.2 = 180,000 viewers
- Week 3: 180,000 1.2 = 216,000 viewers
- Week 4: 216,000 1.2 = 259,200 viewers
- Week 5: 259,200 1.2 = 311,040 viewers
We continue this pattern until the cumulative total of viewings is approximately 5,937,075 viewers.
Summing up the weeks:
- Week 1: 150,000
- Week 2: 150,000 + 180,000 = 330,000
- Week 3: 330,000 + 216,000 = 546,000
- Week 4: 546,000 + 259,200 = 805,200
- Week 5: 805,200 + 311,040 = 1,116,240
Continuing the calculations for further weeks, we can see that:
- ...
- Week 12: will sum to a total viewings figure close to 5,937,075.
From these calculations, the network researchers find that it will take approximately 12 weeks for the number of viewings to reach 5,937,075.
Thus, the correct answer to fill in the blank is "12".
So the completed sentence becomes:
At this rate, there will be approximately 5,937,075 total viewings of the show after 12 weeks.
