SOLUTION: My daughter missed this class friday and has a final monday morning..can you please show how to get answer and correct answer? Superman has a violent reaction to red kryptonite wh

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Question 177441: My daughter missed this class friday and has a final monday morning..can you please show how to get answer and correct answer? Superman has a violent reaction to red kryptonite which decays into green krytonite with a half life of 5 hours. Red Kryptonite is no longer dangerous to Superman when 90 percent of the red kryptonite has decayed.
a. What percent of the kryptonite is left after one day?
b. how long before the red kryptonite has decayed 90 percent and is safe for superman?
Thank you for your help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a.)If you start with 100% and the half life is 5 hours
N%28t%29=N%5B0%5D%2Ae%5E%28-alpha%2At%29
where
alpha=ln%282%29%2Ft%5Bhl%5D=ln%282%29%2F5=0.1386
Then for t=24 hours,
N%28t%29=N%5B0%5D%2Ae%5E%28-alpha%2At%29
N%2824%29=N%5B0%5D%2Ae%5E%28-0.1386%2A24%29
N%2824%29=100%2A0.0359
N%2824%29=3.59
3.59% remains at 24 hours.
b.)Start with 100%. Find t when 90% will be gone, 10% will remain.
N%28t%29=N%5B0%5D%2Ae%5E%28-alpha%2At%29
10=100%2Ae%5E%28-0.1386%2At%29
e%5E%28-0.1386%2At%29=0.1
-0.1386%2At=ln%280.1%29
-0.1386%2At=-2.303
t=-2.303%2F0.1386
t=16.6
After 16.6 hours, there will be 10% left.