# Business MathDerivation of separate formulae for calculation of population growth rates of male and female cattle

#### audax

##### New member
I want to estimate the number of male and female cattle produced over a period of time (say, five years and ten years) from an initial stock of 30 heifers, all 18 months of age at which age they are first joined (mated). Assume that the first calf is born when the mother is 27 months old. Thereafter, a new calf is born every two years. Assume also 100% fertility and survival, new-born calves are 50% male, 50% female and all females are joined at 18 months.

If all calves were female, a birth every two years would be a population growth rate of 50% pa and the calculation would be simple but I don't know how to devise the formulae for female population growth rate and male population growth rate. Can you help?

#### audax

##### New member
It appears that nobody is interested in this topic so I'll close it down. I actually have a much more complicated scenario than I've described and I worked it all out manually so I now don't need any help.

But this looks to be a really useful and interesting site. I'm sure I'll be back.