Question

In the first week of a song's release, it had 16 million streams. each week, the number of streams is 90% of the previous week. how many streams will there be in the sixth week?a. 8,503,056 b. 9,447,840 c. 10,497,600 d. 11,664,000

Answer 1

The number of streams in the sixth week, given an initial count of 16 million and a weekly decay rate of 90%, can be calculated using an exponential decay formula. After performing the calculations, the stream count for the sixth week is found to be approximately 9,447,840. The number of streams in the sixth week will be approximately 9,447,840, which corresponds to option (b).

Step-by-step explanation:

To calculate the number of streams in the sixth week given that the song's streams decrease to 90% of the previous week's streams, we can use the formula for the decay of a quantity over time, which models an exponential decrease:

Stream count of the nth week = initial stream count × (decay rate)^(n - 1)

Here, the initial stream count is 16 million, decay rate is 90% or 0.9, and n is the week number.

For the sixth week (n=6):
16 million × (0.9)^5

Let's calculate step-by-step:

1. 16 million × 0.9 = 14.4 million (for the second week)
2. 14.4 million × 0.9 = 12.96 million (for the third week)
3. 12.96 million × 0.9 = 11.664 million (for the fourth week)
4. 11.664 million × 0.9 = 10.4976 million (for the fifth week)
5. 10.4976 million × 0.9 = 9.44784 million (for the sixth week)

So, the number of streams in the sixth week will be approximately 9,447,840, which corresponds to option (b).

Answer 2

(B) 9,447,840

Step-by-step explanation:

Week Streams

1 16,000,000 x 90

2 14,400,000 x 90

3 12,960,000 x 90

4 11,664,000 x 90

5 10,497,600 x 90

6 9,447,840 x 90

Therefore, the answer would be 9,447,840