SOLUTION: A research assistant made 160 mg of a radioactive substance, and found that there was only 20 mg left after 45 hours. if the researcher knew he needed 100 mg of the same substance

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Question 862432: A research assistant made 160 mg of a radioactive substance, and found that there was only 20 mg left after 45 hours. if the researcher knew he needed 100 mg of the same substance 12 hours after he was able to make a fresh batch, how much should he initially make?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Decay model, 20=160e%5E%28-k%2A45%29, and solve for k to help find a specific formula.
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%281%2F8%29=e%5E%28-k%2A45%29
ln%288%5E%28-1%29%29=-k%2A45
-ln%288%29=-k%2A45
k=ln%288%29%2F45
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highlight%28k=0.0462%29.
Decay equation for this substance is highlight%28A=I%2Ae%5E%28-0.0462%2At%29%29.
A is amount at time t;
I is initial amount, t=0;
t is time in hours.

The question that you want to answer is for t=12, and A=100, what is the initial amount needed, I?