SOLUTION: A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is {{{A(t) = 100(1.5)^(-t)}}} Determine the rate of dec

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Question 1163396: A radioactive substance decays so that after t years, the amount remaining,
expressed as a percent of the original amount, is A%28t%29+=+100%281.5%29%5E%28-t%29
Determine the rate of decay after 2 years. Round to 2 decimal places.

Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A radioactive substance decays so that after t years, the amount remaining,
expressed as a percent of the original amount, is A%28t%29+=+100%281.5%29%5E%28-t%29
Determine the rate of decay after 2 years. Round to 2 decimal places.
:
t = 2
Put this in your calc 100(1.5)^(-2)
44.44 % remain after 2 years

Answer by ikleyn(52932) About Me  (Show Source):
You can put this solution on YOUR website!
.

Exponential rate of decay per year "r" remains THE SAME during the entire decay process 

(i.e. FOREVER, or, more precisely, until the last radioactive atom decayed :-).


It is equal to  r = 1.5%5E%28-1%29 = 1%2F1.5 = 1%2F%28%283%2F2%29%29 = 2%2F3 = 0.666666...  or  66.6666%  of the mass per year.



By the way, when you formulate a problem like this one, you should tell in your question, which rate of decay do you mean:

    exponential coefficient of decay or linear coefficient at the given time.



These are two different values and two different conceptions.


Without clarification, the meaning of the question is dark / unclear.


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What the tutor ankor@dixie-net.com wrote in his response,  was not an answer to your question.

It was something   V E R Y   different.   It was about the remained mass amount after 2 years.


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On radioactive decay problems,  see the lesson
    - Radioactive decay problems
in this site.