A good question about Hogs

I have been asked to find out if something is true: Wether one sow and all of that one sows offspring could replenish the entire worlds population of hogs within the original sows lifetime. It sounds possible considering their large litters, however, I dont know how many hogs there are in the world at any one time, and factors other than human consumption must affect their mortality. Is this possible? Thank You!

If g is the average time between litters for a sow (the gestation period plus a little more to get them pregnant), and 2f is the average size of a litter (so f is the average number of female offspring), then after n gestations periods a time of ng has passed and we have f^(ng) females. So there are twice this many pigs altogether when we count the males too. If the current world pig population is P, we have to find out how long it would take for 2xf^(ng)=P. In other words, solve for n.

Then we see which is longer, the remaining life expectancy of the momma sow or the time ng it would take to repigulate the earth.

You just need to fill in:
g= gestation period of the pig plus an appropriate “impregantion time” (probably you would need to see how long between periods of estrus and add that amount of time to the gestation period to get g).
2f= average litter size
P= current pig population of earth.
I’ve ignored a lot of things here, like disease. You’d be inbreeding pigs, and the survival rate of the litters would probably go down. Also, I’m assuming that if the original momma is still alive, all the kids are too. But that’s probably more detail than you really want. A ballpark answer can be had from the above calculation if you do a little research on pig reproduction numbers.