Home > Student Resources > Solving Word Problems Involving Applications of Sequences and Series

Solving 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 a month.

Step 1: draw

Step 2: Formula

$a_{n}=2^{n}$

Check: $2^{0}=1$ * always start at day 0

$2^{1}=2$

$2^{2}=4$

$2^{3}=8$

Step 3: Summation

$\sum_{n=0}^{30} 2^{n}\ assuming\ month\ =\ 30\ days$

Step 4: Expand

$2^{0}+2^{1}+2^{2}+2^{3}+...+2^{30}$

$\ =2,147,483,647\ >\ 2\ billion\ mm^{2}$

$1\ mm=0.003\ ft$

$1\ mm^{2}=0.000006\ ft^{2}=18,000\ ft^{2}$