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:
[tex]\frac{100\%+6\%}{100\%}=\frac{106\%}{100\%}=1.06[/tex]Then, for the first month the user base will be:
[tex]21,740\times1.06=23,044.4[/tex]Then, for the second month the user base will be:
[tex]23,044.4\times1.06=24,427.06[/tex]The third month would be:
[tex]24,427.06\times1.06=25,892.70[/tex]We could do this for eight months or we can take a shortcut:
[tex]U=U_0\times i^n[/tex]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:
[tex]U=21,740\times1.06^8[/tex][tex]U=34,650.26[/tex]Answer: 34,650.26 users after 8 months with a 6% increase per month.
