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What is the equation for a penny doubling every day for a year?
Wiki User
∙ 14y ago
The equation for the amount you have reached on a given day is 2n-1, where n is the days since starting. For example, on the first day 21-1 = 1 penny, while 2200-1 = 8.035 x 1059 pennies on the two-hundredth day, and 2365-1 = 3.758 x 10109 pennies on the last day.
The equation for the whole amount is Σ1365 (2n-1), where the sigma represents the sum of a series and the range is from day 1 to day 365.
: Another way of looking at it, which doesn't involve scary "sigma" signs, is this:
Whereas X is set equal to "the number of pennies one would receive on the last day of the year after starting with one penny and doubling it every day", then X would equal 2 to the 364th power.
2 to the zeroth power is one. First day.
2 to the first power is two. Second day.
2 to the second power is four. Third day.
2 to the third power is eight. Fourth day.
Etc. Note that each power is one less than the day in question. Therefore, 2 to the 364th power would show you how many pennies you would receive on the 365th day.
However, one must then perform this equation, for the total number of pennies one would have at the end of the year:
2 to the zeroth plus 2 to the first plus 2 to the second...plus 2 to the 362nd plus 2 to the 363rd plus 2 to the 364th = Y, whereas Y is equal to "the total number of pennies one would have at the end of the year".
Yet, an easy short cut is to realize that one need only take the value of X (which is equal to how many pennies you receive on the last day of the year) and subtract one, in order to see how many pennies you had received on the first 364 days of the year total!
Then add that amount to X, and you will have Y (which is equal to the total amount of pennies you have for the whole year). Or, X plus (X-1) = Y.
Wiki User
∙ 14y ago
tomáš “VODKA” Vodičk...
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What does doubling a penny a day for a year equal?
Assuming 365 days: Doubling a penny 365 days means you would have 2365 pennies after 365 days. That's something on the order of 3.76 x 10109 cents, which is about $3.76 x 10107 in cold, hard American cash.
If i give you one penny one day two the next day and keep doubling it for one year how much money would it equal?
If you keep doubling it for one month, you will already have 10737413,11 dollars.
How much will you have if you saved a penny every day for a year?
365 pennies = $3.65
Wats the value of a orange one half penny?
The value of an orange one half penny varies by the year of the penny and the condition.
What is the volume of a pre 1982 penny?
it is unknown becasue of the change of pennys evry year
What does doubling a penny a day for a year equal?
Assuming 365 days: Doubling a penny 365 days means you would have 2365 pennies after 365 days. That's something on the order of 3.76 x 10109 cents, which is about $3.76 x 10107 in cold, hard American cash.
If i give you one penny one day two the next day and keep doubling it for one year how much money would it equal?
If you keep doubling it for one month, you will already have 10737413,11 dollars.
Penny collection - 1857 through 2009 inclusive a penny for every year?
$1.53
You have got a penny from every year to date but not a 1972 was the penny made in 1972?
A LOT of them - around 6 billion, in fact.
How much will you have if you saved a penny every day for a year?
365 pennies = $3.65
How much money does Jared Allen make?
he makes one penny every year
How much is 1966 double die reverse Lincoln cent?
To date, no certified examples of a reverse doubled-die 1966 Lincoln cent exist. Mechanical doubling is likely what you see, not a true doubled-die error. Mechanical doubling is the most common type of doubling on U.S. coins and is most often confused with doubled dies, this doubling is extremely common with numerous examples being produced on all denominations every year. It's value is only what someone is willing to pay.
If you double a penny for a year how much will you have?
Well, doubling your penny could be expressed as 2d where d equals the amount of days you have been doubling. So a year would be 2365 or 7.51533626 X 10109 (109 zeroes). This equates to $751,533,626,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.00 I'm pretty sure that's more than a google. BUT WAIT: THERE'S MORE! If you keep the money from each day, you would need to turn this into a permutation. This means its 2365 X 2264 X 2363X 2362... all the way to 21. This is way too much money and I don't even think there is a name for this number.
How much money to give a 11 year old?
we give our kids a penny- a nickel for every orange they pick up in our backyard
What year was the penny black invented?
The Penny Black was invented in the year 1840 in memory of QUEEN VICTORIA
What is on the back of a penny?
That really depends in what country and what year the penny was minted.
In what year will the 1943 Australian penny worth 1000?
Who knows. If all of a sudden, for some bizarre reason, every coin collector in the world wanted a 1943 Australian Penny, it could be worth $1,000 or more tomorrow.
