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# exponential growth

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1971
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what is the amount of a penny that grows exponentially for 30 days

Sep 18, 2016

#3
+10

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

`

`

`

536,870,912 pennies on day 30

Sep 18, 2016

#1
+10

What is the exponent?    Doubles everyday?   Triples? etc

Sep 18, 2016
#2
+5

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: \({10}^{30}\)

.
Sep 18, 2016
#3
+10

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

`

`

`

536,870,912 pennies on day 30

ElectricPavlov  Sep 18, 2016
#4
+5

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

--------------------------

Remember: “A penny learned is a penny earned” Sep 18, 2016
edited by GingerAle  Sep 18, 2016
#5
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It all depends on how you interpret the question.....I guess both could be viewed as correct.

My view:

If you put the penny in a bank (that would be day 1).....it would not be doubled until the next day (day2).  The penny does not double on the first day....it would be double after 24 hours, otherwise you are STARTING with two pennies.

But I can see it your way too...except if you have a day ZERO and then compute for 30 more days you are using 31 days, not 30.     YMMV !!! ElectricPavlov  Sep 18, 2016
#6
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I guess I would see it better as doubling it 30 TIMES as opposed to doubling it 30 DAYS.  !!!

ElectricPavlov  Sep 18, 2016
#7
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But according to all of our former banking questions the interest rate would be 100% compounded daily for 30 days with an P of 1 cent, which would yield:

Fv = Pv (1+1)^30 = 1 (2)^30 = 107341824 at the end of the 30th day....as y'all calculated.....you are right! ElectricPavlov  Sep 18, 2016