There were 256 people at a fundraiser. When the event was over, half of the people who remained left every 5 minutes.
How long after the event ended did the last person leave?
find how many minutes until one is left. That one leaves immediately if the first ones left at t = 0
a(n+1) = (1/2)A(n)
a(1) = 256
a(N) = 1
an = a1 r^n-1
1 = 256 *.5^(n-1)
.5^(n-1) = 1/256
(n-1) log .5 = log (1/256)
n-1 = 8
n = 9
so 9 * 5 min = 45 min
if the first ones left at the END of the first five minutes then the last one leaves after 50 minutes
To find out how long after the event ended the last person left, we need to determine the number of people who remained after each 5-minute interval and keep track of the time.
Given that there were 256 people at the beginning, we can start by halving this number after every 5-minute interval until there are no people left.
Let's break down the problem step by step:
1. Start with the initial number of people: 256.
2. After the first 5 minutes, half of the people remaining will leave. So, we multiply the current number of remaining people by 0.5:
Remaining after 5 minutes = 256 * 0.5 = 128.
3. After the second 5 minutes, again, half of the remaining people will leave:
Remaining after 10 minutes = 128 * 0.5 = 64.
4. Repeat this process until there are no people left:
Remaining after 15 minutes = 64 * 0.5 = 32
Remaining after 20 minutes = 32 * 0.5 = 16
Remaining after 25 minutes = 16 * 0.5 = 8
Remaining after 30 minutes = 8 * 0.5 = 4
Remaining after 35 minutes = 4 * 0.5 = 2
Remaining after 40 minutes = 2 * 0.5 = 1
So, after 40 minutes, there is only 1 person left. This means that the last person will leave after 40 minutes from the end of the event.