psol := exp(a*(t - 1790))*P0

P t+1 = r * Pt
The mathematical model based on this idea is that the population size for one generation depends on the size of the previous generation, and it is a multiple. This is expressed mathematically by the following equation:

(1)

where:

t represents the time period (which could be minutes, weeks, years, etc. depending on the species being considered),
pt represents the population size at time t. The units of time could be hours, days, years, etc.,
pt+1 represents the population size at the next time period. Again, it could be the next hour, next day, next year, etc., and
r referred to as the Malthusian factor, is the multiple that determines the growth rate