Question

A video is labeled a fan favorite if it receives at least 1,000 views per day. Amelia posts a video that gets 8,192 views on the first day. 3. Suppose the number of views decreases by 20% per day. In how many days will the number of views per day be less than 1,000?

Answer 1

Answer:

It will take 10 days for the views to be less than 1000

Step-by-step explanation:

Given that Amelia posts a video that gets 8,192 views on the first day.

Since the number of views decreases by 20% per day, we have the equation below:

`y=a(1-r)^x`

Where y is a function of x (The time it will take for the number of views to be less than 1000), a is the initial number of views (8,192), and r is the rate at which the views decreases (0.20).

We now have the equation:

`1000=8192(1-0.20)^x`
`\begin{gathered} (1000)/(8192)=0.8^x \\ \\ 0.8^x=0.122 \end{gathered}`

Take logarithms of both sides

`\begin{gathered} x\log (0.8)=\log (0.122) \\ x=(\log (0.122))/(\log (0.8))=9.43 \end{gathered}`

x will surely by less than 1000 views in 10 days