Let's solve the problem step-by-step.
1. Identify the weekly viewers:
- Week 1: 150,000
- Week 2: 180,000
- Week 3: 216,000
- Week 4: 259,200
- Week 5: 311,040
2. Calculate the total number of viewers after 5 weeks:
[tex]\[
\text{Total viewers after 5 weeks} = 150,000 + 180,000 + 216,000 + 259,200 + 311,040 = 1,116,240
\][/tex]
3. Determine the weekly growth rate:
Notice that the viewership seems to be growing exponentially. To find the growth rate, we can calculate the ratio of viewers between two consecutive weeks:
[tex]\[
\text{Growth rate} = \frac{\text{Number of viewers in Week 2}}{\text{Number of viewers in Week 1}} = \frac{180,000}{150,000} = 1.2
\][/tex]
4. Predict future viewership using exponential growth:
We know the total number of viewers after 5 weeks, and we know the growth rate is 1.2. We need to find the number of weeks it takes for the total viewership to reach approximately 5,937,075.
5. Calculate cumulative viewership week by week until the total reaches about 5,937,075:
- Week 6: 311,040 1.2 = 373,248 (total viewers: 1,116,240 + 373,248)
- Week 7: 373,248 1.2 = 447,897.6 (total viewers: sum of previous weeks)
- Week 8: 447,897.6 1.2 = 537,477.12 (total viewers: sum of previous weeks)
- Week 9: 537,477.12 1.2 = 644,972.544 (total viewers: sum of previous weeks)
- Week 10: 644,972.544 1.2 = 773,967.0528 (total viewers: sum of previous weeks)
- Week 11: 773,967.0528 1.2 = 928,760.46336 (total viewers: sum of previous weeks)
- Week 12: 928,760.46336 * 1.2 = 1,114,512.556032 (total viewers: sum of previous weeks)
When adding these numbers cumulatively, after around 12 weeks, the total viewership sums up to about 5,937,075.
So, the correct answer to the question is obtained after approximately:
[tex]\[
\text{Select the correct answer from the drop-down menu: } \boxed{12}
\][/tex]
