The following diagram shows the number of people who know the riddle per day.
The values of x would be from day 1 to 6 while the values of y will be 5, 20, 60, 240, 960, 3840. Thus, we may write the following in the table as follows:
Notice that 5 is always multiplied by a power of 4.
Thus, on day 1, we have
[tex]5(4^0)=5(1)=5[/tex]
On day 2, we have
[tex]5(4^1)=5(4)=20[/tex]
On day 3, we have
[tex]5(4^2)=5(16)=80[/tex]
On day 4, we have
[tex]5(4^3)=5(64)=320[/tex]
On day 5, we have
[tex]5(4^4)=5(256)=1280[/tex]
And on day 6, we have
[tex]5(4^5)=5(1024)=5120[/tex]
Therefore, we may say that the formula to obtain the number of people who know the riddle on x days will be
[tex]y=5(4^{x-1})[/tex]
where y is the number of people and x is the number of days.
Therefore, on the 15th day, we substitute 15 to x in the obtained equation.
[tex]\begin{gathered} y=5(4^{15-1}) \\ =5\mleft(4^{14}\mright) \\ =5(268,435,456) \\ =1,342,177,280 \end{gathered}[/tex]
Therefore, there will be 1,342,177,280 people who will know the answer on the 15th day.
