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 (100)/(100)\dotfill &1\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A = 5000e^(1\cdot t)\implies \boxed{A = 5000e^t}`