Explanation
This question wants us to compute the depreciation formula and also get the value of the total page views did the webpage have after seven days.
The general formula is given by
[tex]A=P(1-\frac{r}{100})^n[/tex]
In our case
[tex]\begin{gathered} A=? \\ P=5000 \\ r=10 \\ n=n \end{gathered}[/tex]
Thus, we will have
[tex]A=5000(1-\frac{10}{100})^n[/tex]
We will now have to write the first three terms of the expression to get the required equation
[tex]\begin{gathered} when\text{ n=1} \\ A_1=5000(0.9)^1=4500 \end{gathered}[/tex][tex]\begin{gathered} when\text{ n=2} \\ A_2=5000(0.9)^2=4050 \end{gathered}[/tex]
Now, we can list the first three terms as
[tex]5000,4500,4050[/tex]
With the above, we can now compute the total web pages after 7 days using the sum of the geometric sequence:
We will get the common ratio
[tex]ratio=r=\frac{4500}{5000}=0.9[/tex]
[tex]\begin{gathered} S=\frac{a(1-r^n)}{1-r} \\ \\ a=5000 \\ r=0.9 \\ n=7 \end{gathered}[/tex]
[tex]S=\frac{5000(1-0.9^7)}{1-0.9}=26085[/tex]
Thus, we can see that the answer is option C
[tex]\frac{5000(1-0.9^7)}{1-0.9}=26,085[/tex]
