You begin to fill a bucket with water at 9 am. Each minute you double the amount of water in the bucket. If it takes you 1 hour to fill the bucket, at what time is the bucket one-quarter full?
it's full at 10
half full at 9:59
a quarter full at 9:58
9:58 one-quarter full
9:59 half full
10:00 full
To find out at what time the bucket is one-quarter full, we need to figure out how many minutes it will take to reach that mark.
Let's assume that at 9 am, the bucket is empty. From this point, we double the amount of water in the bucket each minute. So, after the first minute, we will have 1 unit of water in the bucket.
After the second minute, the amount of water doubles again, so we will have 2 units.
Following the pattern, we can determine that after N minutes, we will have 2^N units of water in the bucket.
Now, let's figure out when the bucket will be one-quarter full. This means we want to find the value of N when the amount of water in the bucket is equal to one-quarter of the final amount when it is full.
Let's represent the final amount of water in the bucket when it is full as F.
Since the amount of water doubles each minute, F is equal to 2^60 because there are 60 minutes in an hour.
To find the number of minutes required for the bucket to be one-quarter full, we need to solve the equation: (1/4)F = 2^N.
Substituting the values, we have: (1/4)(2^60) = 2^N.
Simplifying the equation, we get: 2^N = (1/4)(2^60).
To solve for N, we take the logarithm of both sides of the equation: log2(2^N) = log2((1/4)(2^60)).
Using the logarithmic property, we can simplify the equation: N = log2(1/4) + log2(2^60).
Since log2(1/4) is -2 (2 raised to what power gives us 1/4) and log2(2^60) is 60, we have: N = -2 + 60.
So, N = 58.
Therefore, it will take 58 minutes to fill one-quarter of the bucket. Therefore, if you started filling the bucket at 9 am, the bucket would be one-quarter full at 9:58 am.