Question

Can someone help me out with this?

Answer 1

`\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{(t)/(c)}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &1000\\ r=rate\to 50\%\to (50)/(100)\dotfill &(1)/(2)\\ t=\textit{seconds}\\ c=period\dotfill &5.5 \end{cases} \\\\\\ A=1000(1 - (1)/(2))^{(t)/(5.5)}\implies A=1000((1)/(2))^{(t)/(5.5)}\hspace{3em}\textit{halving every 5.5 seconds}`