The relationship between initial and final herd sizes, assuming compound growth, is
Initial herd size × (1 + x) ^ n = Final herd size
where x is the annual growth rate and n is the time interval in years. The caret (^) signifies exponentiation, one plus x raised to the nth power.
Solving for x,
x = 10 ^ [1 ÷ n × log(Final herd size ÷ Initial herd size)] – 1
Multiply the result by 100 to obtain a growth rate in percent per year.
The math is a little tedious to do by hand so let’s set it up in a spreadsheet.
In Excel, the formula in cell B9 is =100*(10^(1/B7*LOG(B5/B3))-1). The other cells are just text and numbers. If you use different cells for the data, the formula won’t work.
You can copy the formula and paste it into your spreadsheet, starting with = but don’t include the period. The number format for cell B9 was set to one decimal place.
The post from December 16 included two examples. In the second case, a herd of 100 wild horses becomes a herd of 201 wild horses in five years if the annual growth rate is 15% per year. Those numbers were used to test the spreadsheet.
AMLs are often specified as a range, with the lower end about half of the upper end, to allow for a doubling of the herd size in four or five years.
The proposed AML for the Heber WHT is 50 – 104. If you start with 50 wild horses and find 104 wild horses in four years, what was the annual growth rate?
The Heber AML is discussed on page 21 of the new management plan.
RELATED: More On Growth Rates.