Respuesta :
[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]
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]
The number of members after six years is 1600.
We have given that,
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.
What is the formula for exponential growth?
[tex]A=P(1+r)^t[/tex]
A=Amount
P=initial amount
r=rate
t=time
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]A=25(1+1)^6\\A=25(2)^6\\A=1600[/tex]
Therefore we get the number of members after six years is 1600.
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