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Solve Word Problems Involving Applications of Sequences and Series

You have a petri dish with 1 square millimeter of a mold that doubles in size every day. What area will it cover in 1 month?

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$\begin{equation*} a_n = 2^n \end{equation*}$

Check:

*Always start at day 0

$\begin{equation*} 2^0 = 1 \end{equation*}$

$\begin{equation*} 2^1 = 2 \end{equation*}$

$\begin{equation*} 2^2 = 4 \end{equation*}$

$\begin{equation*} 2^3 = 8 \end{equation*}$

$\begin{equation*} \sum_{n=0}^{30} 2^n \end{equation*}$

assuming month = 30 days

$\begin{equation*} 2^0 + 2^1 + 2^2 + 2^3 + \dots + 2^{30} \end{equation*}$

$\begin{equation*} = \boxed{2,147,483,647} > 2 \text{ billion mm}^2 \end{equation*}$

$\begin{equation*} 1 \text{mm} = 0.003 \text{ft} \end{equation*}$

$\begin{equation*} 1 \text{mm}^2 = 0.000006 \text{ft}^2 \end{equation*}$

$\begin{equation*} = 18,000 \text{ft}^2 \end{equation*}$