"Published in Suisun City, California, USA"
A very patient woman wishes to become a billionaire. She decides to follow a simple scheme: She puts aside 1 cent the first day, 2 cents the second day, 4 cents the third day, and so on, doubling the number of cents each day. How much money will she have at the end of 30 days? How many days will it take this woman to realize her wish?
Solution:
From the given word problem, let's analyze the statements as follows
1st Day = 1 cent
2nd Day = 2 cents
3rd Day = 4 cents
4th Day = 8 cents
5th Day = 16 cents
.
.
.
and so on
As you noticed that everyday she double the money that she put for her scheme. The given word problem is an application of Geometric Progression because the sequence has a common ratio which is 2.
Let a = 1
r = 2
The Sum of Geometric Progression is given by the formula
where n = nth term in the sequence
Consider again the word problem that if a woman is following her scheme for 30 days, the total amount of her money will be as follows
Substitute a = 1, r = 2, and n = 30 to the above equation, we have
Therefore, in 30 days, she will earn 1,073,741,823 cents or US $ 10,737,418.23.
If she wants to become a billionaire, she must continue her scheme as follows
Take Natural Logarithm on both sides on the equation
Therefore, she will be a billionaire for 37 days!