What would you do?
Option 1
You can have $1,000,000
Yeah, that's right a million bucks!!!
Option 2
You can have 1 penny doubled every day for 30 days.
Come on, just give me a million dollars!
I've always been kind of partial to pennies!
Explanation and Best Answer
Option 1) $1,000,000
Option 2) is an exponential growth function y = 2x (in pennies).
229 = 536870912 pennies
= $ 536870912/100 dollars
= $5,368,709.12
| Day | Sum |
|---|---|
| 1 | $.01 or (20 in pennies) |
| 2 | $.02 or (21 in pennies) |
| 3 | $.04 |
| 4 | $.08 |
| 5 | $.16 |
| 6 | $.32 |
| 7 | $.64 |
| 8 | $1.28 |
| 9 | $2.56 |
| 10 | $5.12 |
| 11 | $10.24 |
| 12 | $20.48 |
| 13 | $40.96 |
| 14 | $81.92 |
| 15 | $163.84 |
| 16 | $327.68 |
| 17 | $655.36 |
| 18 | $1,310.72 |
| 19 | $2,621.44 |
| 20 | $5,242.88 |
| 21 | $10,485.76 |
| 22 | $20,971.52 |
| 23 | $41,943.04 |
| 24 | $83,886.08 |
| 25 | $167,772.16 |
| 26 | $335,544.32 |
| 27 | $671,088.64 |
| 28 | $1,342,177.28 |
| 29 | $2,684,354.56 |
| 30 | $5,368,709.12 |
This question demonstrates the trait that we keep coming back to: exponential growth might not start out with much (1 and 2 dollars in the first years), but eventually its rate of growth is humongous!
