Suppose you discover a magical U.S. quarter (25 cent piece)

Question

Suppose you discover a magical U.S. quarter (25 cent piece) that has the power to double (in quantity) each day when placed in fertile soil. After being planted in the soil for one day you now have 2 quarters, after two days you have 4 quarters, after three days you have 8 quarters, and so on. What is the dollar value of the quarters after 20 days?

Suppose you discover a magical U.S. quarter (25 cent piece) that has the power to double (in quantity) each day when placed in fertile soil. After being planted in the soil for one day you now have 2 quarters, after two days you have 4 quarters, after three days you have 8 quarters, and so on. What is the dollar value of the quarters after 20 days?

Answer 1

Hi Taylor.

 

This is an exponential growth problem. The number of quarters, Q(n), you'll have after "n" days is given by:

 

Q(n) = 2ⁿ

 

n = 0, Q = 2⁰ = 1 quarter

n = 1, Q = 2¹ = 2 quarters

n = 2, Q = 2² = 4 quarters

n = 3, Q = 2³ = 8 quarters

 

and so on.

 

You want to know the dollar value after 20 days. First you need to figure out how many quarters you'll have:

 

Q(20) = 2²⁰ quarters

 

Now you can determine the dollar amount of your stash. The value of each quarter is 1/4 dollar.

 

So in dollars, you'll have:

 

$ = 2²⁰ quarters * (1/4) dollar/quarter

 

= 2²⁰ * (1/2)²

 

= $2¹⁸ 

 

= $262,144

 

That's a pretty awesome quarter.

 

Hope this helps.