How was the supplied result arrived at?

[Aussiebear]

In the attached workbook is a table which is meant to determine the projected increase in mite populations for a given variable over 12 months. The table below is simply a copy of the table within the workbook. I am trying to calculate how the supplied result was achieved. My best guess and its only a guess, to calculate the Overall fold increase is to use the formula


=Round(Month+ (Month*0.021),0)

Which is only accurate for the first 6 months then it goes astray.



Month
r Value
Overall Fold increase
Supplied Result


1
0.021
=Round(A2+(A2*B2),0)
1


2
0.021

2


3
0.021

4


4
0.021

7


5
0.021

12


6
0.021

23


7
0.021

44


8
0.021

82


9
-0.005

154


10
-0.005

133


11
-0.005

114


12
-0.005

98


13
-0.005

85



Could someone help me understand how to construct the correct formula please?

[Aussiebear]

My bad.... here is the workbook

[p45cal]

I suspect the supplied results are the results of counting mites in the field (hive?)??
I think I can explain how some of these numbers could be calculated:
the r value is like what the bank quotes you when they say you get 5% interest per year. Using that 5% per year you can calculate what your money will be in a year's time; you simply multiply your starting amount by 1.05. That 1.05 comes from 5% (=.05) plus 1. After the second year your money will be:
your initial sum *1.05 * 1.05, or initial sum * 1.05 ^2 (squared),
after three years it'll be: initial sum * 1.05 ^3 etc.

The r value of .021 is 2.1% increase, but it's per day. The left hand column is in months, so the monthly increase is:
the previous month's population * 1.021^30
where the 30 is the number of days in a month (whether 30, or an average number of days in a month, or the actual number of days in the month concerned has been used, I don't know).

See attached workbook where I've added a couple of columns where column H might be something like how a population column might be created.

ref: https://scientificbeekeeping.com/the-varroa-problem-part-11/

[Aussiebear]

Having spent some more time with this issue, it appears that the creator of the Workbook may have used the following formula.



=Previous Month Population * EXP(r.Value* 30)


and then rounded back to an integer.