The principle of exponential growth (decay of kyrponite)

[Guest]

Superman has a violent reaction to red kryptonite which decays into green kryptonite, fortunately with a half-life of 15 hours. When 90% of the red kryptonite has decayed, it is no longer dangerous to Superman. If Superman is exposed to pure red kryptonite, for how long is he in danger? Use the model A=A0e^kt.


I got 9.9 hours which can not possibly be right if the half life is 15 hours. Can someone help and explain this to me. Thanks

 

[galactus]

First, you can find the constant k:

Since we know the 1/2 life is 15 hrs.

\(\displaystyle \frac{A}{2}=Ae^{15k}\)

\(\displaystyle \frac{1}{2}=e^{15k}\)

\(\displaystyle k=\frac{-ln(2)}{15}\approx{-0.0462098}\)


Now, if 90% has decayed, then there is 10% left.

Set up your formula and solve for t.