During an experiment, the number of organisms present at time $t$ days is denoted by $N$, where $N$ is treated as a continuous variable. It is given that
$\frac{{dN}}{{dt}} = 1.2{e^{0.02t}}{N^{0.5}}$.
When $t = 0$, the number of organisms present is 100.
a) Find an expression for $N$ in terms of $t$.
b) State what happens to the number of organisms present after a long time.
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