Half-Life Problem: Solving A0e13K to Get K

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1. Half life of a radioactive substance is 13 days. How long for 400 grams to decay to 300 grams? Solve algebraically and show all work. Give both exact answers and the answer rounded to 4 decimal places.



So I manipulated (1/2)A0=A0e13K to obtain K = ln(1/2)/13

Where do I go from here?
 
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lwelch70 said:
1. Half life of a radioactive substance is 13 days. How long for 400 grams to decay to 300 grams? Solve algebraically and show all work. Give both exact answers and the answer rounded to 4 decimal places.



So I manipulated (1/2)A0=A0e13K to obtain K = ln(1/2)/13

Where do I go from here?

Put your known numbers back in the equation:

A = A0e(kt)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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