First, find an expression for the number of page views for the n-th day.
Since each day the number of visitors decreases by 12%, then, the number of page views is 88% of the number of visitors from the previous day. We can find that amount by multiplying 3000 by 0.88.
The n-th day, that amount would have been multiplied by 0.88 n-1 times (the first day, it is multiplied by a factor of 0.88^0, the second day, by 0.88^1, and so on, so the n-th day, the amount of visitors can be found by multiplying by a factor of 0.88^n-1).
Then, the expression for the number of visitors of the n-th day is:
[tex]v_n=3000\cdot0.88^{n-1}[/tex]
On the other hand, remember the following formula:
[tex]r^0+r^1+r^2+...+r^{n-1}=\frac{1-r^n}{1-r}[/tex]
The amount of visitors after nine days can be found as:
[tex]\begin{gathered} v_1+v_2+...+v_9 \\ =3000\times0.88^0+3000\times0.88^1+...+3000\times0.88^8 \\ =3000\times(0.88^0+0.88^1+...+0.88^8) \\ =3000\times\left(\frac{1-0.88^9}{1-0.88}\right) \\ =17,088.04045... \\ \approx17,088 \end{gathered}[/tex]
Therefore, the correct choice is:
[tex]3000\left(\frac{1-0.88^9}{1-0.88}\right)\approx17,088[/tex]
