Question

a company launches its new website and tracks the number of visits to the site. predict the number of visits on the 10th day.
day number of visits
1 12
2 18
3 26
4 41
5 61
about 500
about 1000
about 5000
about 10,000

Explanation:

Step1: Analyze the growth pattern

Looking at the number of visits: from day 1 to day 2, the increase is \(18 - 12=6\); from day 2 to day 3, the increase is \(26 - 18 = 8\); from day 3 to day 4, the increase is \(41-26 = 15\); from day 4 to day 5, the increase is \(61 - 41=20\). The growth is accelerating. If we assume an exponential - like growth (a rough estimate for business website visit growth).

Step2: Estimate the 10th - day visits

We know that the growth is non - linear. If we consider a very rough exponential growth model (since the increments are getting larger). If we assume that the growth factor is increasing.
If we consider that from day 5 to day 10, the growth is much larger. If we assume a very simple doubling - like (not exact) growth pattern (for a quick estimate).
From day 1 (\(n = 1\), \(y=12\)) to day 5 (\(n = 5\), \(y = 61\)). If we assume a function \(y=a\times b^{n}+c\) (a very basic exponential - like form).
Another way is to note that the values are increasing more than linearly. If we consider that from day 5 (\(y = 61\)) to day 10 (5 days later), if we assume that the growth rate per day is such that the number of visits more than doubles a few times.
If we assume a very rough geometric - sequence - like growth (not a perfect fit but for estimation). If we consider that the number of visits from day 5 to day 10:
If we assume that the number of visits on day 6 is about \(61\times1.5=91.5\), day 7: \(91.5\times1.5 = 137.25\), day 8: \(137.25\times1.5=205.875\), day 9: \(205.875\times1.5 = 308.8125\), day 10: \(308.8125\times1.5=463.21875\) (this is a very simple multiplier, but if we consider a more aggressive growth factor).
If we consider that the growth from day 1 to day 5: \(12\) to \(61\) (approximate \(5\) times in 4 days). If we assume that from day 5 to day 10 (5 days), if the growth is such that it is about \(16\) times (a very rough estimate based on the fact that the growth is accelerating). \(61\times16 = 976\approx1000\)

Answer:

about 1000