How was the supplied result arrived at?

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

Code:

---

=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?

My bad.... here is the workbook

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...oblem-part-11/

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

Code:

---

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

---

and then rounded back to an integer.