Half Life and Decay
New to this forum so let me know If I am doing anything wrong.
My question: Ive decided to take a calculus course after many years of not doing any math.. If you can give me hints in regards to this question it would be greatly appreciated.
A 96-milligram sample of a radioactive substance decays according to the equation
N=96 ·e-0.034 ·t where N is the number of milligrams present after t years.
(a) Find the half-life of the substance to the nearest tenth of a year.
Thank you very much.
Oh man, I need to review my logs
To summarize, I am given K or some variable. Plug known variable in and solve for Time in this case. I understand looking at your steps, but I have a stupid question to ask:
Why do we ln both sides again? Was it to bring down the exponent?
Its been a really, really, long time..
Yes; the only way to get the power down where you could work with it was to take logs. (Wink)
Yeah, and logs and exponentials are inverse operations like adding and subtracting.
Originally Posted by mvho
In my post everything except the last two lines is deriving the general half life formula so if you don't need to know it's derivation you can stick with
k will always be the number next to t and will be a power along with t as well as k > 0. The units will be 1 over the units of k for any exponent must be dimensionless. If k is in per minute, t will be in minutes
Thanks everyone. Never even knew this site existed, will have to share with everyone.
Math is funny; once you get going, it seems all your tools come back pretty quickly.