Question

a company launches a new website and tracks the number of visits to the site. predict the number of visits on the 8th day.
day number of visits
1 40
2 160
3 640
4 2650
5 10,240
about 100,000
about 150,000
about 200,000
about 650,000

Explanation:

Step1: Find the pattern

We observe that \(40\times4 = 160\), \(160\times4=640\), \(640\times 4 = 2560\) (there might be a typo in the given data for day 4, it should be \(2560\) as per the pattern), \(2560\times4=10240\). So the pattern is that the number of visits each day is \(4\) times the number of visits of the previous day. The general formula for the \(n\)th - day is \(a_{n}=a_{1}\times4^{n - 1}\), where \(a_{1}=40\) (the number of visits on day 1) and \(n\) is the day number.

Step2: Calculate for \(n = 8\)

Substitute \(n = 8\) into the formula \(a_{n}=40\times4^{n - 1}\). Then \(a_{8}=40\times4^{8 - 1}=40\times4^{7}\).
We know that \(4^{7}=4\times4\times4\times4\times4\times4\times4=16384\).
So \(a_{8}=40\times16384 = 655360\approx650000\)

Answer:

about 650,000