00:01
Okay, so here we have a physical example of what half -life is, where we're removing half the pennies each time the box is shaken.
00:09
So the data that we have, we can go ahead and see.
00:17
We did six trials, and we have tails and heads, and tails are being removed from the box.
00:30
So initially, we started with zero tails and 100 heads.
00:34
So this represents our starting amount.
00:37
For trial two we had 24 tails and 76 heads and then we had 14 tails and 62 heads.
00:49
Then we had 21 tails and 41 heads and then 18 tails and 23 heads and then six tails and 17 heads.
01:03
And what we want to know is what the half -life of pentium is in our experiment.
01:07
So we've gone through one, two, three, four, five half -lifes each time the box is shaken and so what we can do is we can use the half -life equation to calculate what the half -life of pennium what the half -life of penium is so here we have our amount at time t is equal to the amount that we started with times one -half times t over t one -half so we started with 100 and we ended with 17 and the time elapsed was six, we did six trials.
02:46
And so what we can do to solve for half -life is we're going to need to use log rules to bring down the exponent, but first we can go ahead and simplify our numbers.
02:55
So we have 17 divided by 100, which is 0 .17, and this is equal to our one -half component.
03:14
So to bring this down, we can take the log of each side, so log of 0 .17 is going to be equal to six trials divided by the half -life times the log of 1 -half...