Question

134. Учёные вывели новую разновидность бактерий. Каждую секунду любая бактерия делится на две. В ходе эксперимента было выяснено, что если в пробирку поместить одну бактерию, то через 64 секунды пробирка заполнится. Через какое время заполнится пробирка, если в неё поместить шестнадцать бактерий?

Answer 1

За 60 секунд 16 бактерий заполнят пробирку.

За 4 секунды 1 бактерия размножается до 16 (1*2*2*2*2),  поэтому их нужно вычесть из 64 секунд.

Answer 2

получаеться что пробирка заполнится за 2 секунды. Тоесть 16*2 и 32*2. Это если в пробирке 1 бактерия и он всё заполнила за 64 секунды. Ну наверно так.

Answer 3

Calculation of Bacterial Growth

To determine how long it will take for a test tube to be filled with bacteria, given that each bacterium divides into two every second, we can use the concept of exponential growth.

Let's break down the problem step by step:

1. Initially, there is one bacterium in the test tube. 2. After 1 second, the bacterium divides into two, resulting in a total of two bacteria. 3. After 2 seconds, each of the two bacteria divides into two, resulting in a total of four bacteria. 4. After 3 seconds, each of the four bacteria divides into two, resulting in a total of eight bacteria. 5. This pattern continues, with the number of bacteria doubling every second.

Now, let's calculate how long it will take for the test tube to be filled if we start with 16 bacteria.

Calculation:

Starting with 16 bacteria, we need to determine how many times the number of bacteria doubles until the test tube is filled.

Since the number of bacteria doubles every second, we can use the formula:

Number of bacteria = Initial number of bacteria * 2^(time in seconds)

Let's solve for time:

16 * 2^time = capacity of the test tube

To find the time it takes for the test tube to be filled, we need to solve for time. We know that the test tube is filled after 64 seconds when starting with 1 bacterium.

16 * 2^time = 2^6

Dividing both sides by 16:

2^time = 2^6 / 16

Simplifying:

2^time = 2^6 / 2^4

Using the property of exponents (division):

2^time = 2^(6-4)

Since the bases are the same, the exponents must be equal:

time = 6 - 4

time = 2 seconds

Therefore, if we start with 16 bacteria, it will take 2 seconds for the test tube to be filled.

Please note that this calculation assumes ideal conditions and does not take into account factors such as bacterial competition, limited resources, or other environmental factors that may affect bacterial growth rates.