00:01
In this problem, we're told that a biologist finds that the population of a certain type of bacteria is going to be able to double every half hour.
00:07
So we're told that the initial amount of bacteria in a culture was 52 bacteria.
00:12
We want to know what the population would be after five hours.
00:16
Well, what we want to do first is write a function to help us find the population at any given time.
00:21
So we have a general formula for this.
00:24
It's p of t equals p -0, the initial amount, times two, choose our base because it's doubling, raised to the t over n power, where t is the number of hours, and n is the half -life.
00:36
So for our function, we'll have p of t equals p -subs -0 is the initial amount, which is 50, and then we'll have two raised to the t over, or half -life time is a half -hour, so 0 .5.
00:47
So now that we have our function, we can find how much is in there after five hours by substituting in five for t.
00:54
So a p of 5 equal to 50 times 2 raised to the 5 divided by 0 .0.
01:01
So now we can go to our calculator.
01:04
So 50 and then in parentheses, 2 raised to the 5 divided by 0 .5 power would be 51 ,200.
01:11
So that's how many bacteria there will be after 5 hours.
01:15
Next, i'll call this part b.
01:17
We want to figure out how many hours it's going to take for there to be 204 ,800 bacteria...