Dog video viewers

Question

Trying to use summation formula to find a pattern between video viewers on day 1, 500 viewers, day 2, 751 viewers, day 3, 1124 viewers and day 4, 1688 viewers and I’m trying to figure out based on this pattern what the viewers would be each day for a total of 14 days.

Answer 1

The first thing to do, and often the hardest, is to find some sort of relationship between the terms of the sequence.

A good way to start is the look at the 1st difference, then the second difference, 3rd difference, and so forth.

Since the 1st difference is not the same, this is NOT a linear function.

Since the 2nd difference is not the same, this is NOT a quadratic function.

Unfortunately, we don't have enough terms to take any more differences.

We can use a TI-84 calculator to test other possibilities fairly easily.

Plug the numbers into a "list" like this (using "stat" then "edit" "1:Edit"):

L1 | L2

----------|-------------

1 | 500

2 | 751

3 | 1124

4 | 1688

Then use "stat" "CALC" "6:CubicReg" to find out if this is a cubic function. You should get the following:

y=ax³+bx²+cx+d

a=11.5

b=-8

c=194.5

d=302

R²=1

An "R²" of 1 means a perfect fit so the relationship is a cubic function with those values for the coefficients.

So you could use:

14

∑ (11.5x³ - 8x² + 194.5x + 302)

x=1

I got an answer larger than 143,000