Math Is Fun Forum

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

The Penguin Problem:

Jane finds that there are 1,000 penguins on Lup Island.
Find a formula for determining how many penguins will be there in 7 years.
1) The penguin colony consists of equal amounts of male and female penguins.
2) The penguins form couples( a male and a female) and have one baby every Spring.
3) A 1/5 of the penguin population(adults and babies) dies at the end of every year.
4) 1 year old penguins will also form couples.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

So, there are 500 couples to start?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: The Penguin Problem:

Yes.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

So next year these 500 penguin pairs each have one baby penguin? What is the probability of having a male penguin born?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: The Penguin Problem:

1000(1.2)^(x-1), apparently, is the formula(1000 is the starting amount, and I don't know why .2 is the growth rate for these penguins.
Let me clarify by showing how the second year of penguins grow:
first: 1000, 1500 penguins, 1200 penguins(300dead)
second: 1200 penguins, 1800 penguins, 1440 penguins(360 dead)(900 males, 900 females).

Last edited by Mathegocart (2017-01-29 12:45:55)

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

You have to be saying that every year an equal amount of males and females is born?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

You have to be saying that every year an equal amount of males and females is born?

...and also accept the existence of partial penguins?

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

Plentiful Partial Penguins is a Paradoxically Perplexing Problem.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Plentiful Partial Penguins is a Paradoxically Perplexing Problem.

Provokingly put.

Properly processed, partial-penguin portions' participation produces precise population poll projection.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

Ponderous Passages Produce Pericardial Palpitations.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Perhaps. Prudent prose perusers phare phar phiner.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

phare phar phiner?

Phi Phi Pho Phum.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Kermit the Phrog and Phozzie Bear - Phootloose and Phancy-Phree

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

I can not top that, you win.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

It was phun.

Nice little song, that, by a great team.

Last edited by phrontister (2017-01-30 04:03:17)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

koushikghosh19

Member

Registered: 2017-01-30

Posts: 1

Re: The Penguin Problem:

If total number of penguins is x.
Year 1 : x (original number of penguins) + x/2 (the babies) - x/5 (dead penguins) = x+3x/10
Year 2 : (x+3x/10) + 3(x+3x/10)/10 = x+3x/10+3x/10+9x/100 = x+2*3x/10+(3x/10)² = (x+3x/10)²
Year 3 : well I don't have the patience to do further

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

Hi; koushikghosh19;

Are you not assuming that exactly half the babies are male? How do we know that?

Hi Phrontister;

Phantastic Phun Phorall.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Hi Bobby;

You got Me on that one!

Penguin Puzzle Phormula: in the case that halPh the babies are Phemale (and ignoring the Partial Penguin conundrum), we could use a compound interest Phormula, covered by MIPH here. It works.

Last edited by phrontister (2017-01-30 10:39:45)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

What haPPens iPh an odd number oPh Penguins are born?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Then they can't do this:

4) 1 year old penguins will also form couples.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

There are two kinds of problems in the world...ones I can solve and ones I cannot.

There are two more types of problems in the world...ones that are clearly defined and ones that are a bit vague.

Then there are two more types of problems in the world...

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

...ones that require the wisdom of Solomon and ones that don't.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Penguin Problem:

That is two more.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: The Penguin Problem:

Hi koushikghosh19, and welcome to the forum!

If total number of penguins is x.
Year 1 : x (original number of penguins) + x/2 (the babies) - x/5 (dead penguins) = x+3x/10

Your dead penguin count is incorrect, as it doesn't include babies:

3) A 1/5 of the penguin population(adults and babies) dies at the end of every year.

Last edited by phrontister (2017-01-31 12:11:43)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson