It'll be half full in 4 hours.
When will it be 1/4 full? Remember that it doubles every hour.
full capacity within 8hours, in how many hours was it filled to one quarter of its capacity?
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When will it be 1/4 full? Remember that it doubles every hour.
If we denote the initial volume of the swimming pool as "V," after 1 hour it would be 2V (doubled), after 2 hours it would be 4V (doubled again), and so on.
Now, we need to determine how many hours it took for the pool to be filled to one-quarter of its capacity.
To do this, let's consider the fraction of capacity filled at each hour. After 1 hour, the pool is filled to 1/2 of its capacity (2V/4V = 1/2). After 2 hours, it is filled to 1/4 (4V/4V = 1), and after 3 hours, it is filled to 1/8 (8V/4V = 1/8).
From this analysis, we can see a pattern emerging. The fraction of capacity filled after n hours is given by 1/2^n.
Since we want to determine the number of hours it took to fill one-quarter of the capacity, we need to solve the equation 1/2^n = 1/4.
To simplify the equation, we can rewrite 1/4 as 2^-2 (since 2^-2 = 1/4).
Now, we have the equation 1/2^n = 2^-2.
To solve this equation, we can set the exponents equal to each other:
n = -2
Therefore, it took the pool -2 hours to be filled to one-quarter of its capacity.
However, this doesn't make physical sense since time cannot be negative. This means that the pool was never filled to one-quarter of its capacity, given the doubling rate of the volume of water every hour.