Bacteria in a glass !

[Sriman Dutta]

Suppose a glass tumbler contains a certain number of bacteria. A scientist found that the number of bacteria doubles itself after every one second by asexual reproduction (completely hypothetical). He observed that after one minute the glass was full of bacteria. Can anyone tell when was the glass half-full ?

[DrKrettin]

59 seconds

[Function]

I am first of all very glad that you speak of hypothetical situations; bacteria who divide in one second, marvellous ... (For the sake of completing my cynism: 20-30 minutes is a plausible convention on bacterial replication cycle duration)

 

By logical reasoning, you can easily get what DrKrettin has answered ...

 

If you were to solve it by equation:

 

Given the reproduction of each bacteria: 1 generation each second: the number doubles each second.

 

If you'd like to write down the number of bacteria in function of the time, you could write

 

[math]N(t) = n_0 \cdot 2^t[/math]

 

With N(t) the number of bacteria and t the time, in seconds and [math]n_0[/math] the original number of bacteria.

 

After 1 minute, t = 60

 

[math]N_{60} = n_0 \cdot 2^{60}[/math]

 

Now, you want to know at which time N is half of this number, so:

 

[math]N_t = n_0 \cdot 2^t = \frac{N_{60}}{2} = \frac{n_0 \cdot 2^{60}}{2} = n_0 \cdot 2^{59}[/math]

 

Ergo, t = 59 seconds.

Edited October 24, 2016 by Function

[Raider5678]

Suppose a glass tumbler contains a certain number of bacteria. A scientist found that the number of bacteria doubles itself after every one second by asexual reproduction (completely hypothetical). He observed that after one minute the glass was full of bacteria. Can anyone tell when was the glass half-full ?

And to cover this, 1 glass ~ 2 cups. 80 seconds later

61 seconds : 4 cups

62: 8 cups

63: 16 cups = 1 gallon

64: 2 gallons

65: 4 gallons

66: 8 gallons

16 Gallons

32 gallons

64 gallons

70 : 128 gallons

256 gallons > 1 cubic meter

2 cubic meters

4 cubic meters

8 cubic meters

75 :16 cubic meters

32 cubic meters

64 cubic meters

128 Cubic meter

256 Cubic meters

80 :512 cubic meters

1024 cubic meters

2048 cubic meters

4096 cubic meters

~~~8000 cubic meters

85: 16000 cubic meters

32000 cubic meters

64000 cubic meters

1.28 e5

2.56 e5

90 :5.12 e5

1,000,000 cubic meters

2 e6

4 e6

8 e6

95 : 1.6 e7

3.2 e7

6.4 e7

128,000,000

256,000,000

100 : 512,000,000

~~~~ 1 cubic kilometer

2,4,8,(105)16,32,64,128,256,(110)512,1024,2048,4096, ~~~ 8000, (115)16000, 32000, 64000, 128000, 256000,(120) 512000, 1 million cubic kilometers

2,4,8,(125)16,32,64,128,256,(130)512,1024,2048,4096, ~~~ 8000, (135)16000, 32000, 64000, 128000, 256000, (140)512000, 1 billion cubic kilometers

~~~~ All the water on earths oceans.

[Function]

And to cover this, 1 glass ~ 2 cups. 80 seconds later

61 seconds : 4 cups

62: 8 cups

63: 16 cups = 1 gallon

64: 2 gallons

65: 4 gallons

66: 8 gallons

16 Gallons

32 gallons

64 gallons

70 : 128 gallons

256 gallons > 1 cubic meter

2 cubic meters

4 cubic meters

8 cubic meters

75 :16 cubic meters

32 cubic meters

64 cubic meters

128 Cubic meter

256 Cubic meters

80 :512 cubic meters

1024 cubic meters

2048 cubic meters

4096 cubic meters

~~~8000 cubic meters

85: 16000 cubic meters

32000 cubic meters

64000 cubic meters

1.28 e5

2.56 e5

90 :5.12 e5

1,000,000 cubic meters

2 e6

4 e6

8 e6

95 : 1.6 e7

3.2 e7

6.4 e7

128,000,000

256,000,000

100 : 512,000,000

~~~~ 1 cubic kilometer

2,4,8,(105)16,32,64,128,256,(110)512,1024,2048,4096, ~~~ 8000, (115)16000, 32000, 64000, 128000, 256000,(120) 512000, 1 million cubic kilometers

2,4,8,(125)16,32,64,128,256,(130)512,1024,2048,4096, ~~~ 8000, (135)16000, 32000, 64000, 128000, 256000, (140)512000, 1 billion cubic kilometers

~~~~ All the water on earths oceans.

 

That is, on the assumption that 16 cups equals 1 gallon.

[Sriman Dutta]

Well done Dr. Krettin and Function.

Wonderful calculations Raider.

[Raider5678]

 

That is, on the assumption that 16 cups equals 1 gallon.

This is wrong how my friend?

[imatfaal]

This is wrong how my friend?

 

There are different gallons? And those on the actual continent of Europe use the fiendishly clever SI where none of that is necessary (in the UK we are stuck in between with grams of sugar, pints of milk, and gallons of beer (and they are different and strangely big gallons)

[DrKrettin]

 

There are different gallons? And those on the actual continent of Europe use the fiendishly clever SI where none of that is necessary (in the UK we are stuck in between with grams of sugar, pints of milk, and gallons of beer (and they are different and strangely big gallons)

 

 

Never mind, we are inching towards the metric system.

[Function]

 

There are different gallons? And those on the actual continent of Europe use the fiendishly clever SI where none of that is necessary (in the UK we are stuck in between with grams of sugar, pints of milk, and gallons of beer (and they are different and strangely big gallons)

 

Ah, well, I was taught the metric system and have never had a clue about what for heaven's sake a gallon was. I thought it was like a steady unit, convertable to litres?

 

What I meant, was that it differs based on size of the cup (yes, we Europeans are known to have different cup sizes!). But if a gallon is indeed expressed in quantities of a certain volume (e.g. x cups/bottles/tanks/swimming pools), then I will of course retreat my former reaction in a most humble way, not knowing the exact definition of a gallon.

Edited October 25, 2016 by Function

[imatfaal]

 

Ah, well, I was taught the metric system and have never had a clue about what for heaven's sake a gallon was. I thought it was like a steady unit, convertable to litres?

What I meant, was that It differs based on size of the cup. But if a gallon is indeed expressed in quantities of a certain volume (e.g. x cups/bottles/tanks/swimming pools), then I will of course retreat my former reaction in a most humble way, not knowing the exact definition of a gallon.

 

There is the imperial gallon (what Brits used to measure petrol and stuff like that in) and there is the US gallon (which the Mercans still use to measure petrol etc.) The imperial gallon is 4.55 litres. The US gallon is 3.79 litres

 

 

The cup is either 236 millilitres or 240 millilitres depending on your exact definition ( US customary or US official).

 

So there are four different "numbers of cups per gallon" - however only an American would use the term and in that case there are 16 cups per gallon

[Function]

 

There is the imperial gallon (what Brits used to measure petrol and stuff like that in) and there is the US gallon (which the Mercans still use to measure petrol etc.) The imperial gallon is 4.55 litres. The US gallon is 3.79 litres

 

 

The cup is either 236 millilitres or 240 millilitres depending on your exact definition ( US customary or US official).

 

So there are four different "numbers of cups per gallon" - however only an American would use the term and in that case there are 16 cups per gallon

 

Holy crap I couldn't handle all that complicated mess :')

Thanks for the explanation!

[imatfaal]

Never mind, we are inching towards the metric system.

 

Groan. Took me a while to get that.

 

BTW - you are upstaging me on poetry concerning the Pierian Spring :-D

[Raider5678]

 

Groan. Took me a while to get that.

Or you could have just asked the local Mercan. You know, either or. You could have also used this helpful thing called google

[DrKrettin]

 

BTW - you are upstaging me on poetry concerning the Pierian Spring :-D

 

Wow - I didn't think anybody would get that!

[imatfaal]

Or you could have just asked the local Mercan. You know, either or. You could have also used this helpful thing called google

 

whoosh!

---

 

 

Wow - I didn't think anybody would get that!

 

Work for Greek company, been to Lesbos more times than I can remember, and can read just enough Greek script to recognize names, places etc.

[DrKrettin]

 

whoosh!

---

 

 

Work for Greek company, been to Lesbos more times than I can remember, and can read just enough Greek script to recognize names, places etc.

 

I assumed you were familiar with Lesbian dialect of 600 BC

[imatfaal]

 

I assumed you were familiar with Lesbian dialect of 600 BC

 

No - but I hope that I am not someone who does not love poetry

[StringJunky]

 

 

Never mind, we are inching towards the metric system.

I'll drink my pint to that.

[imatfaal]

I'll drink my pint to that.

 

I remember a drunken lunchtime discussion with disputants claiming that we would never move to litres etc for beer. The main reason was that "a pint" was just too integral to the language and no one would ever say "fancy a demi?" "a demi of ordinary please" "just down the local for a demi with John" etc. The Guardian reading Liberal pinkos disagreed and wanted to embrace the continental colloquialisms whilst the UKIP/Brexit/Dinosaur part of the debate all agreed vocally that we would never use the term demi instead of pint - it was too stupid and we don't talk like that. They then spoilt the argument by asking "anyone want a swift half for the road?"

[DrKrettin]

Ignoring the more important issue of English beer being warm, lifeless and undrinkable, it reminds me of the outrage when weather forecasting moved from fahrenheit to celcius, when dinosaurs objected that they could no longer use expressions like "temperatures in the eighties". It was surprising how quickly most people got used to celcius equivalents. Here (Spain) beer is either large or small, and I don't actually know how many ml that means.

[StringJunky]

 

I remember a drunken lunchtime discussion with disputants claiming that we would never move to litres etc for beer. The main reason was that "a pint" was just too integral to the language and no one would ever say "fancy a demi?" "a demi of ordinary please" "just down the local for a demi with John" etc. The Guardian reading Liberal pinkos disagreed and wanted to embrace the continental colloquialisms whilst the UKIP/Brexit/Dinosaur part of the debate all agreed vocally that we would never use the term demi instead of pint - it was too stupid and we don't talk like that. They then spoilt the argument by asking "anyone want a swift half for the road?"

It just shows. how rooted it is. In fishing line strengths and fish weights it's all pounds, even with kids that otherwise use metric. They do, however, say e.g. "16 point 4 pounds" instead of "16 4" meaning 16 pounds 4 ounces; even adults make this mistake.

Edited October 26, 2016 by StringJunky