Question

On the day a video was posted online, 5 people watched the video. The next month the number of viewers had doubled. Assume the number of viewers continues to double each day.

1) How many viewers will be there in one year? Use commas. Show your reasoning.
2) Estimate on which day will 640 people see the video? Show your reasoning.

Answer 1

Explanation:

Given

When video is posted 5 people watched it

Next day number of viewers doubled

Suppose this trend continues i.e. No of viewers doubled each day

So on 2 nd day no of viewers is
`2* 5`

On 3rd day , viewers
`2^2* 5`

on n th day , viewers is
`2^(n-1)* 5`

So no of viewers in 1 year i.e. on 365 day

`=2^(365-1)* 5`

`=2^(364)* 5`

(ii)Day on which 640 people seen the video

`2^(n-1)* 5=640`

`2^(n-1)=128`

`2^(n-1)=2^7`

Therefore

`n-1=7`

`n=8\ days`