what are some assumptions that have to be made when predicting population?

2 answers

You have to assume that the present rate of population growth (or decline), since the last census, will continue. You also have to assume that the previous census was accurate.
Are you talking about human population or modelling population growth in general?

In general population growth modelling you will need to look at factors affecting fitness, such as food supply, predation, disease etc. The same factors are also used for modelling human population growth. Some of these can be estimated with some confidence, some cannot.

Two factors that can be estimated are:
the age structure of the population and
the total fertility rate (TFR).

Total Fertility Rate (TFR)
The total fertility rate is the average number of children that each woman will have during her lifetime. The TFR is an average because, of course, some women will have more, some fewer, and some no children at all.

Theoretically, when the TFR = 2, each pair of parents just replaces itself.

As an example there has been a decline in total fertility rates (TFRs) in undeveloped countries, presumably as the various factors involved in the demographic transition take hold, e.g.,
improved standard of living
increased confidence that your children will survive to maturity
improved status of women
increased use of birth control measures