## ← Computing Half-Life - Differential Equations in Action

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

1. If T equals the half-life, this vector has to be one half, so that the number of particles remaining is half of
2. the initial number of particles. So we get this equation: E to the minus half-life divided by 20 seconds,
3. equals one half. And now you take the natural logarithm on both sides and get minus half-life,
4. divided by 20 seconds, equals the natural logarithm of one half.
5. You bring over the minus and the 20 seconds to the right-hand side, and what you get is the half life is
6. minus 20 seconds times the natural logarithm of one half.
7. So this one is correct. But that's not the only one that's correct.
8. The next one is two. If you found the logarithm of an inverse, you get minus the logarithm of that number.
9. Remember, if you form an inverse, one over A, that would be E to the minus B.
10. So the logarithm of the inverse is minus B.
11. If the logarithm of the number as such is plus B.
12. These two yield the same result. The last one can't be true because it has a different sign than the one before, which is correct.
13. In the first one we're dividing by a number that's smaller than one.
14. So we get something that's larger than 20 seconds, which can't be true, because we know that the lifetime,
15. 20 seconds, has to be larger than the half-life.