The number of concert tickets sold doubles every hour. After 12 hours, all of the tickets are sold. After how many hours are about one-fourth of the tickets sold? Explain your reasoning.

It's 10 hours

To determine the number of hours it takes to sell about one-fourth of the tickets, we need to break down the problem into steps:

Step 1: Calculate the number of tickets sold after 12 hours
Given that the number of tickets sold doubles every hour, we can calculate the total number of tickets sold after 12 hours by repeatedly multiplying the initial number of tickets by 2.

Let's assume the initial number of tickets is "x." After 1 hour, the number of tickets sold is 2x, after 2 hours it is 4x, after 3 hours it is 8x, and so on. Therefore, after 12 hours, the number of tickets sold is 2^12 * x, which simplifies to 4096x.

Step 2: Calculate one-fourth of the tickets sold after 12 hours
To find one-fourth of the tickets sold after 12 hours, we divide the number of tickets sold after 12 hours by 4:

(1/4) * 4096x = 1024x

Therefore, after 12 hours, one-fourth of the tickets sold would be 1024x.

Step 3: Calculate the number of hours it takes to sell about one-fourth of the tickets
Since the number of tickets sold doubles every hour, we can start with one-fourth of the tickets sold after 12 hours (1024x) and work backward to find the number of hours it takes to reach that point.

Let's call the number of hours it takes to sell about one-fourth of the tickets "h." After h hours, the number of tickets sold would be 2^h * x.

So, 2^h * x = 1024x

Dividing both sides by x, we get:

2^h = 1024

To solve for h, we can take the logarithm of both sides with base 2:

log2(2^h) = log2(1024)

h * log2(2) = log2(1024)

Since log2(2) equals 1, we can simplify the equation to:

h = log2(1024)

Using a calculator or computer, we find that log2(1024) is equal to 10.

Therefore, it would take approximately 10 hours to sell about one-fourth of the concert tickets.

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