00:01
All right this problem is asking you to identify a colony of bacteria that's growing exponentially, doubling in size every 140 minutes.
00:11
How many minutes will it take for the colony of bacteria to become five times its current size? they're not giving you much information at all, but what you want to do is start out with this very generic exponential function.
00:26
All right so everyone's aware here this is the initial amount where it begins.
00:32
All right this is going to be your final amount kind of where it ends up.
00:37
E, well e's the number 2 .718281828.
00:41
K is going to be your growth rate or decay rate.
00:45
If it's growing it's going to be a positive k value.
00:47
If it's decaying it's going to be a negative k value.
00:51
And t represents some kind of time.
00:56
All right so a colony of bacteria is growing exponentially.
00:59
It's doubling in size every 140 minutes.
01:02
Literally the only thing they're giving you here is t.
01:05
They're only giving you time.
01:06
We just don't know where it begins.
01:08
We know it starts at a.
01:10
Could be a one, could be a hundred, could be a million.
01:12
We don't know, but all we know is it wants to double.
01:15
So whatever it begins at it's going to be twice that.
01:19
E is e.
01:21
K is what we're solving for because we don't know the rate that it's actually doubling.
01:25
We just know that it takes 140 minutes.
01:27
So in a typical problem like this you want to isolate the e.
01:32
So the first thing we're going to do is divide by a.
01:35
So that 2 equals e to the, i'll just clean that up, 140k.
01:41
We like seeing numbers in front of the letters.
01:43
And because this is a natural base e i want to take a natural logarithm on each side to solve.
01:52
We should know that exponents come down in front because of the power property of logarithms and that the natural log of e is 1.
02:04
And since it's 1 i can multiply, divide, divide by 1...