Amoeba spliting

the last second it doubled from a half to full room therefore 3600-1=3599

This question should be worded differently. According to the statement only one amoeba is doubling.

Can amoeba fill the remaining half in just a second, that is half the room and also why is amoeba referred to as he? :)

Just for fun:

$\text{Mass of amoeba} \approx 10 ^ {-8} \text{grams}$ $\text{Volume of amoeba} \approx 10 ^ {-8} \text{grams}\ / \text{water density} = 10^{-8} \text{cm}^3$

$\text{Volume after 3600 seconds}$ $\approx 10^{-8} \text{cm}^3 \times 2^{3600}$

$\approx 10 ^ {989} \times \text{Volume of Universe}$

Also, some time during the third minute, the amoebae will collapse into a black hole.

Let N(t) be bacteria count at any time 't' According to the question,we have N(t)=2^t. Now when the room is full ,t=3600 & N=2^3600,Where N is the bacteria count when the room is full.Now when the room is half filled, n(t)=N/2 or, 2^t=(2^3600)/2 On solving we get t=3599. It is quite fascinating 2 observe that Half of the remaining bacteria multiplies in just a second. That's the power of exponential increment!!

From the information the question gives us, we know that:

• it doubles every second
• after one second the amoeba fills half the room, it doubles so it would fill the whole room.
• it would fill the room in 1 hour.

Therefore the room would be half full 1 second before 1 hour, which is 3600 seconds, so the room would be full after 3600-1=3599 seconds. :)

Every second the number of amoeba doubles, that is there

is 1 amoeba at the 0th second

2 amoeba at the 1st second

4 amoeba at the 2nd second

and so on.

At the xth second, there are 2^x amoeba

Let's say in 1 hour there are 2^n amoeba

then half of the room would be (2^n)/2 amoeba and

this would be simply the second before an hour.

As amoeba duplicates itself every second, we would have: 1 second = 2 amoebas; 2 seconds = 4 amoebas; 3 seconds = 8 amoebas; so.....we would have 2^n amoebas at n seconds. Within 1 hour = 3600 seconds, we would have the amoeba filled full the room with 2^3600 amoebas, suppose t is the time the amoebas​ fill up half the room, we would have 2^3600 = 2*2^t. Solving this equation, we would have t = 3599.

The time it would take for the amoeba to fill up the room is 3600 seconds. This is obtained by multiplying 60 seconds by 60 minutes (there are 60 seconds in a minute and 60 minutes in an hour). Knowing that the amoeba self-double each second, we can state that half a room was filled in 3599 seconds, one second less than 3600. (Except if only 1 amoeba had split. It is possible with how the problem is worded. This would mean that it will take double the time, which would be 7199 seconds.)

All amoebas replicate themselves each second. If in 3600 seconds the room was filled, it means that the previous second contained half the amount of amoebas. 3600 - 1 = 3599

Démosle la vuelta al enunciado. 2^3600 amebas llenan una habitación. Si el número de amebas se divide por 2 cada segundo, ¿en qué segundo habrá la mitad de amebas? La respuesta es obvia.

3600-1=3599