Question

Suppose you send out your newest "tweet" to your 5000 Twitter followers. You suspect that the change in the number of followers that have seen your tweet is proportional to the ratio of the number of followers that have seen the tweet and the number of followers that have not seen the tweet. If 10 followers have seen the tweet 5. after 1 minute, write a differential equation that models the number of followers that have seen the tweet, including any initial condition. [Do not solve the differential equation.]

Answer 1

Answer: Suppose we send out our newest "tweet" to our 5000 Twitter followers.

If 10 followers have seen the tweet after 1 minute, then the differential equation can be written as ;

Let us first assume that at time "t" , "n" followers have seen this tweet.

So, no. of follower who have not seen this tweet are given as : 5000 - n

ratio =
`(n)/(5000 - n)`

∴ we get ,

`(\delta x)/(\delta t)` ∝
`(n)/(5000 - n)`

`(\delta x)/(\delta t)` = k×
`(n)/(5000 - n)` ------ (1)

where k is the proportionality constant

At t = 0 , one follower has seen the tweet.

So n(0) = 0 ------ (2)

So n(1) = 10 ------ (3)

∴ equation (1), (2) and (3) together model the no. of followers that have seen the tweet.