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 20 about 500 about 1000 about 5000 about 10,000

Explanation:

Step1: Analyze the growth pattern

Looking at the number of visits:
Day 1: 12
Day 2: 18 (increase of \(18 - 12=6\))
Day 3: 26 (increase of \(26 - 18 = 8\))
Day 4: 41 (increase of \(41-26 = 15\))
Day 5: 61 (increase of \(61 - 41=20\))

If we assume an exponential - like growth (since the differences between consecutive terms are increasing non - linearly). A rough estimate:
Let's consider a simple exponential model \(y = a\times b^{x}\). Using the first two points \((x = 1,y = 12)\) and \((x = 2,y = 18)\)
If \(y=a\times b^{x}\), then \(12=a\times b^{1}\) and \(18=a\times b^{2}\). Dividing the second equation by the first: \(\frac{a\times b^{2}}{a\times b^{1}}=\frac{18}{12}\), so \(b = 1.5\) and \(a=\frac{12}{1.5}=8\)

The formula is \(y = 8\times(1.5)^{x}\)

Step2: Calculate for \(x = 10\)

Substitute \(x = 10\) into \(y = 8\times(1.5)^{x}\)
\(y=8\times(1.5)^{10}\)
\((1.5)^{10}=57.6650390625\)
\(y=8\times57.6650390625 = 461.3203125\approx500\)

Answer:

about 500