SOLUTION: An initial amount of radioactive substance Yo is given, along with information about the amount remaining after a given time (t). For an equation of the form y=Yo^ekt that models

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Question 892783: An initial amount of radioactive substance Yo is given, along with information about the amount remaining after a given time (t). For an equation of the form y=Yo^ekt that models the situation, give exact value of K in terms of natural log. Yo=30g g; after 6hrs, 10g remaining
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Stick with the lower-case, k. This will become a negative value according to the form for the decay model you seem to want. You are expecting to use highlight_green%28y=Yo%2Ae%5E%28kt%29%29.

You want to find k, knowing Yo, t, and y.
Just solve your equation in general, outlined in green shown earlier, for k. THEN substitute your values for Yo, t, and y.

ln%28y%29=ln%28Yo%2Ae%5E%28kt%29%29
ln%28Yo%29%2Bln%28e%5E%28kt%29%29=ln%28y%29
ln%28e%5E%28kt%29%29%2Bln%28Yo%29=ln%28y%29
kt%2Aln%28e%29%2Bln%28Yo%29=ln%28y%29
kt%2A1=ln%28y%29-ln%28Yo%29
highlight%28highlight%28k=%281%2Ft%29ln%28y%2FYo%29%29%29