The bacteria is in 7 liters container double every 3 minutes. After 54 minutes the container is full. How long did it take to fill a 1/4 of the container?

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To find out how long it took to fill a 1/4 of the container, we need to determine how long it took for the bacteria to fill 1/4 of the container. Let's break down the problem and calculate step by step.

First, we know that the bacteria doubles in population every 3 minutes. So, let's figure out how many times the bacteria population doubles during the 54 minutes it takes to fill the container.

54 minutes divided by 3 minutes (the time it takes for the bacteria to double) equals 18. This means that the bacteria population doubles 18 times during the 54 minutes.

Now, let's determine the final volume of the container after 54 minutes of bacteria growth. We know the starting volume is 7 liters, and we need to add the doubling effect 18 times. We can calculate the final volume by multiplying the starting volume by 2 raised to the power of the number of doublings.

Final volume = Starting volume * (2 ^ Number of doublings)
Final volume = 7 liters * (2 ^ 18)

Calculating this, we find that the final volume after 54 minutes is approximately 377.49 liters.

Next, let's calculate how long it took for 1/4 of the container to be filled. Since the final volume is 377.49 liters, we can find 1/4 of that volume by dividing it by 4.

1/4 of the final volume = 377.49 liters / 4 = 94.37 liters.

To determine how long it took to fill 1/4 of the container, we need to work backward. We know that the initial volume was 7 liters, and the doubling happens every 3 minutes. Let's calculate how many doublings it took to reach 94.37 liters.

94.37 liters divided by 7 liters (initial volume) equals 13.48.

So, approximately 13.48 doublings were needed to reach 94.37 liters.

Now, we know that each doubling takes 3 minutes. Therefore, we can calculate the time it took to reach 13.48 doublings by multiplying 13.48 by 3.

Time to fill 1/4 of the container = 13.48 doublings * 3 minutes per doubling

Calculating this, we find that it took approximately 40.44 minutes to fill 1/4 of the container.

Therefore, it took approximately 40.44 minutes to fill 1/4 of the container.