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.
Tenth hour = 512
Twelfth hour = 2048
2048/4 equals 512
Therefore the tenth hour.
1/4 of the tickets are sold after the tenth hour
2 * (1/4) = 1/2 sold after the eleventh hour
2 * (1/2) = 1 sold after the twelfth hour
How do you get that? That doesn't make sense if all the tickets are sold in 12 hours.
To solve this problem, we can start by finding the total number of tickets sold after 12 hours. Then, we need to determine after how many hours approximately one-fourth of the tickets are sold.
Let's break down the steps:
Step 1: Find the total number of tickets sold after 12 hours.
Since the number of tickets sold doubles every hour, we can use exponential growth to calculate the total number of tickets sold after 12 hours. We start with an initial value of 1 and double it 12 times:
1 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 4096
Hence, after 12 hours, a total of 4096 tickets are sold.
Step 2: Determine after how many hours approximately one-fourth of the tickets are sold.
To find out the number of tickets sold after a certain number of hours, we will use exponential growth as well. We need to find the number of hours, let's call it "t," where the total number of tickets sold is approximately one-fourth (¼) of the tickets sold in 12 hours.
1/4 * 4096 = 1024
We want to determine how many times we need to double the initial value (1) to reach 1024. So, we set up the equation:
1 * (2^t) = 1024
Now, we can solve for "t" by taking the logarithm of both sides:
log(2^t) = log(1024)
t * log(2) = log(1024)
t = log(1024) / log(2)
Using a calculator, we can find:
t ≈ 10
Therefore, approximately one-fourth of the concert tickets will be sold after about 10 hours.
So, after solving the equation, we find that one-fourth of the tickets are sold after approximately 10 hours.