starting with 25 members a club doubled its membership every year write the function f(n) that expresses the number of members after six years

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}[/tex]

now, we know they're doubling every year, so the rate of growth is 100%, so whatever amount, + 100% is just double that much, therefore,

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &25\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &6\\ \end{cases} \\\\\\ A=25(1+1)^6\implies A=25(2)^6\implies A=1600[/tex]