00:01
This question wants us to look at how long something that's growing exponentially will take to grow three times its size.
00:08
So if something's growing exponentially, it follows the form a, the amount is equal to a not, the original amount, times e to the kt, where k is the growth rate and t is time.
00:20
And if we're looking at something that's tripling in size, what we have is that a is equal to three times the original amount, a not.
00:28
So we want to solve an equation for the time when a is equal to 3a0.
00:38
Of course we don't know what k is, so our answer will be in terms of k.
00:45
The original equation that we have is 3a0 is equal to a knot e to the k t.
00:52
Right away, i see that i can divide both sides by a not to get rid of that unknown variable.
00:59
What we'll be left with is 3 equals e to the k t.
01:03
Now, i'm solving for t, so i want to get it out of the exponent...