Question

a. create a table showing the amount of people knowing the answer to the riddle of the six days (1st sketch a diagram to discover the pattern for this problem)b. state the amount of people to know the answer on day 15.

Answer 1

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

$5(4^0)=5(1)=5$

On day 2, we have

$5(4^1)=5(4)=20$

On day 3, we have

$5(4^2)=5(16)=80$

On day 4, we have

$5(4^3)=5(64)=320$

On day 5, we have

$5(4^4)=5(256)=1280$

And on day 6, we have

$5(4^5)=5(1024)=5120$

Therefore, we may say that the formula to obtain the number of people who know the riddle on x days will be

$y=5(4^{x-1})$

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.

$\begin{gathered} y=5(4^{15-1}) \\ =5\mleft(4^{14}\mright) \\ =5(268,435,456) \\ =1,342,177,280 \end{gathered}$

Therefore, there will be 1,342,177,280 people who will know the answer on the 15th day.