Question

A colony of bees doubles in size every month. If there are initially 5000 bee, create a model for the bee population

Answer 1

we know that the colony is doubling, namely the rate of growth is 100% of whatever is existent, thus

$\textit{Amount of Population Growth} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A = 5000e^{1\cdot t}\implies \boxed{A = 5000e^t}$