Question

Hello, can someone please help me?

Answer 1

hmmmm well, if one amoeba becomes two in 24 hours, by splitting or otherwise, then we can say that the rate of growth is 100%, since 2 is 1 + 100% of 1, thus

$\qquad \underset{\textit{for 8 days}}{\textit{Amount for Exponential Growth}} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=days\dotfill &8\\ \end{cases} \\\\\\ A=1(1 + 1)^{8}\implies \boxed{A=256} \\\\[-0.35em] ~\dotfill$

$\qquad \underset{\textit{for 16 days}}{\textit{Amount for Exponential Growth}} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=days\dotfill &8\\ \end{cases} \\\\\\ A=1(1 + 1)^{16}\implies \boxed{A=65536}$