00:01
We are told that a sample bacteria is decaying according to the half -life model.
00:05
In the half -life model, we know that the half -life raised to the time elapsed, divided by the half -life of the bacteria, multiplying that by the initial amount, gives the amount remaining.
00:18
We were told that there were 900 initial bacteria, and then after 10 minutes, there were 630 bacteria remaining.
00:27
We need to find out how many minutes until 30.
00:30
Bacteria remaining.
00:32
So the first thing we need to do is solve for k.
00:34
We want to get k by itself, so we're going to divide each side by 900.
00:41
That gives us 0 .7 equals 0 .5 raise the 10 over k.
00:49
We need to set up a logarithm to figure out the exponent.
00:53
So log base 0 .5 of 0 .7 will equal 10 divided by k.
01:01
Log base 5 of 0 .7 is about equal to 0 .54145.
01:11
And we want to figure out what k is...