Question

analyzing doubling time
if the cells continue to double every 5 minutes, how long will it take to fill 3 additional bottles of the same size?
minutes

Explanation:

Step1: Analyze the doubling - growth

Since the cells double every 5 minutes. To fill 1 bottle from an empty state, assume the initial amount is 1 unit and the full - bottle amount is $x$ units. After the first 5 minutes, the amount is 2 units, after 10 minutes, it is 4 units, and so on. We can think of it in terms of powers of 2. To fill 3 additional bottles, we need to increase the amount by a factor equivalent to filling 3 bottles.

Step2: Determine the number of doublings

We know that $2^n$ represents the amount of growth after $n$ doublings. To fill 3 bottles, we note that $2^2=4$. If we start from a state where we have enough cells to fill 1 bottle, we need 2 more doublings to get enough cells to fill 4 bottles (which is 3 more bottles than the initial 1 - bottle state).

Step3: Calculate the time

Since each doubling takes 5 minutes and we need 2 doublings, the total time $t = 5\times2$.
$t=10$

Answer:

10