exponential growth

If it starts at 1 and doubles everyday:

.01 on day 1

.02 on day 2

.04 on day 3

.08 on day 4

16

32

64

`

`

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536,870,912 pennies on day 30

What is the exponent?    Doubles everyday?   Triples? etc

If you mean the penny's value doubles every day, then do this: \(0.01*{2}^{30}\)

Since \(0.01*{2}^{30}\) = 10 737 418.24, the penny would be worth that much in 30 days.

However, you have not specified what the exponent is. So, just replace the base of \({2}^{30}\) with whatever your exponent is. If the penny's value x10 every day, then change it to: \({10}^{30}\)

EP what you write here really can’t be true.

If it starts at 1 and doubles everyday:

.01 on day 1

. . .

If the amount (a penny on day one) doubles everyday how can you have the same amount? It did not double on day one.  (This reminds me of a few crooked bankers).

Start with a penny on day “zero.” The decimal counting system starts with zero, not one (1). If you look at it this way, it’s more clear.

            _{(Expanding the window will align the text and numbers)}

                                                                    Comparsion to

Day               2^(day number)                      Total grains (of rice) on a chess board,

                                                                    where the previous square’s amounts are added.

                                                                    Note the first square is square zero.

 0                             1                                             1

1                              2                                             3

2                              4                                             7

3                              8                                            15

4                              16                                          31

 . . .                         . . .                                          . . .

28                           268435456                           536870911

29                           536870912                           1073741823

30                           1073741824                         2147483647

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Remember: “A penny learned is a penny earned”