Question

A streaming show is gaining viewers each week. The viewership can be modeled by the equation V = 122 w3 where w is the number of weeks since the show started, and V is thousands of viewers. Select the two sets of steps that you could use to predict when viewership would reach 100,000

Answer 1

To predict when the viewership would reach 100,000, substitute V with 100,000 in the equation V = 122w^3, rearrange the equation to solve for w, and find that viewership would reach 100,000 in approximately 9.45 weeks.

Step-by-step explanation:

To predict when the viewership would reach 100,000, we can set up the given equation V = 122w^3 and substitute V with 100,000.

100,000 = 122w^3

We can rearrange the equation to solve for w.

w^3 = 100,000/122

w^3 = 819.67

By taking the cube root of both sides, we find that w is approximately equal to 9.45.

Therefore, viewership would reach 100,000 in approximately 9.45 weeks.

Answer 2

To predict when the viewership would reach 100,000, we need to solve for w in the equation V = 122w^3 when V is set to 100,000. After finding w^3 = 0.81967, we calculate the cube root to find that w is approximately 0.935 weeks.

Step-by-step explanation:

The student asked how to predict when the viewership of a streaming show would reach 100,000 viewers, given the relationship V = 122w3, where V is the number of viewers in thousands and w is the number of weeks since the show started. To find when the viewership will reach 100,000, we need to solve for w when V equals 100 (since V is given in thousands).

Setting V = 100, we get:

1. 100 = 122w3
2. w3 = 100 / 122
3. w3 = 0.81967
4. w = ∛(0.81967)
5. w ≈ 0.935 (This would be the cube root of 0.81967)

Then, we need to interpret this result. Since the cube root of 0.81967 is approximately 0.935, viewership would reach 100,000 after about 0.935 weeks.