Predictions of Malthus' model

This applet shows predictions of the Malthus' model, [math]N_{t+1}=p N_t[/math], corresponding to different values of [math]N_0[/math] and [math]p[/math].

Observe how the number of individuals [math]N_t[/math] changes with time for different values ​​of [math]p[/math] and of [math]N_0[/math]. Find the function [math]N(x)[/math] which allows directly calculate the value of [math]N_t[/math] from [math]N_0[/math], [math]p[/math], and [math]t[/math], [math]N_t = N(t)[/math], without calculating the intermediate values ​​from [math]N_1[/math] to [math]N_ {t-1}[/math], and enter it in the input box. Remember that to let GeoGebra consider it as a function you have to use [math]x[/math] instead ot [math]t[/math].