#### 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 year for 30 days

### Explanation and Best Answer

**Option 1) **$1,000,000

This would give you $20,000.

**Option 2) **is an exponential growth function y = 2^{x}(in pennies)

2

^{29} = 536870912 pennies

= $ 536870912/100 dollars

** = $5,368,709.12**
Day by Day break Down

Day
1: $.01 or ( 2

^{0} in pennies)

Day
2: $.02 or ( 2

^{1} in pennies)

Day
3: $.04

Day
4: $.08

Day
5: $.16

Day
6: $.32

Day
7: $.64

Day
8: $1.28

Day
9: $2.56

Day
10: $5.12

Day
11: $10.24

Day
12: $20.48

Day
13: $40.96

Day
14: $81.92

Day
15: $163.84

Day
16: $327.68

Day
17: $655.36

Day
18: $1,310.72

Day
19: $2,621.44

Day
20: $5,242.88

Day
21: $10,485.76

Day
22: $20,971.52

Day
23: $41,943.04

Day
24: $83,886.08

Day
25: $167,772.16

Day
26: $335,544.32

Day
27: $671,088.64

Day
28: $1,342,177.28

Day
29: $2,684,354.56

Day
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!