What does this quantity measure?

30 Views Asked by At

Consider this list of numbers:

$$\begin{bmatrix} 59 \\ 148 & 0.60 \\ 200 & 0.26 & 1 \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & 0.10 & 1.8 \\ 400 & 0.10 & 2 \\ 440 & 0.09 & 2.2 \\ 480 & 0.08 & 2.4 \\ 520 & 0.08 & 2.6\\ 568 & 0.08 & 2.84\\ 620 & 0.08 & 3.1 \\ 675 & 0.08 & 3.375 \end{bmatrix}$$

Note that the second column is the $\%$ growth from the previous time period. So $0.60 = (148-59)/148 = 0.6$.

What is the significance of the third column? Is it just normalizing how the rate of growth is changing from each time period?

Added We could aldo consider a fourth column that has things like $(148-59)/59$ instead of $(148-59)/148$. Then it seems that the third column is of the form $(1+r_1)(1+r_2)$.

1

There are 1 best solutions below

2
On

I don't know why it's important, but the third column is the first column divided by $200$.

I figured it out from looking at the rows in red. I don't know why the numbers in green were missing, but it bothered me, so I fixed it.

$$\begin{bmatrix} 59 & \color{green}{0.00} & \color{green}{0.295}\\ 148 & 0.60 & \color{green}{0.74}\\ \color{red}{200} & 0.26 & \color{red}{1} \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & 0.10 & 1.8 \\ \color{red}{400} & 0.10 & \color{red}{2} \\ 440 & 0.09 & 2.2 \\ 480 & 0.08 & 2.4 \\ 520 & 0.08 & 2.6\\ 568 & 0.08 & 2.84\\ 620 & 0.08 & 3.1 \\ 675 & 0.08 & 3.375 \end{bmatrix}$$