Question

A new social media site is increasing its user base by approximately 6% per month.Ir the site currently has 21,740 users, what will the approximate user base be 8 months from now?

Answer 1

Data

• Increase: 6% per month

,

• Current users: 21,740

,

• Users after 8 months: ?

Procedure

As we are increasing 6%, we have to multiply the original quantity, which represents the 100%, times 100% plus the increase (6%). However, this must be done in decimals:

`(100\%+6\%)/(100\%)=(106\%)/(100\%)=1.06`

Then, for the first month the user base will be:

`21,740*1.06=23,044.4`

Then, for the second month the user base will be:

`23,044.4*1.06=24,427.06`

The third month would be:

`24,427.06*1.06=25,892.70`

We could do this for eight months or we can take a shortcut:

`U=U_0* i^n`

where U represents the user, U0 is the initial users, i is the increase rate, and n is the number of months.

Replacing the data we have we get:

`U=21,740*1.06^8`
`U=34,650.26`

Answer: 34,650.26 users after 8 months with a 6% increase per month.