SOLUTION: "A storage tank contains a liquid radioactive element with a half life of 100 years. It will be relatively safe for the contents to leak from the tank when 0.01% of the radioactive
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Question 813607: "A storage tank contains a liquid radioactive element with a half life of 100 years. It will be relatively safe for the contents to leak from the tank when 0.01% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?"
I tried to set up the problem any way I could, For example, I tried to solve like this: f(t)=(.0001)^(t/100), but I couldn't get the answer. I don't understand what I'm doing wrong. The back of the textbooks says that the answer is "1329 years" but I couldn't get the same answer no matter how many different ways I tried to solve it. This problem is in Jay Lehmann's "Intermediate Algebra 4th edition" textbook under section 5.4 "Using the Power Property with Exponential models to Make Predictions" if that helps. A TI83 or TI84 calculator may be required for this problem. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A storage tank contains a liquid radioactive element with a half life of 100 years.
It will be relatively safe for the contents to leak from the tank when 0.01% of the radioactive element remains.
How long must the tank remain intact for this storage procedure to be safe?"
:
Using the radioactive decay formula: A = Ao*2^(-t/h), where:
A = Amt remaining after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
:
Let initial amt = 1, then resulting amt = .0001
2^(-t/100) = .0001 *log(2) = log(.0001) =
using a calc = -13.2877
t = -13.2877 * -100
t = +1328.77 rounds to 1329 yrs
