SOLUTION: Radioactive Decay. The amount of radioactive material, in grams, present after t days is modeled by A(t)=6000e^-.05t (A)Find the amount present after 12 days (B)Find the half

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Question 771049: Radioactive Decay. The amount of radioactive material, in grams, present after t days is modeled by A(t)=6000e^-.05t
(A)Find the amount present after 12 days
(B)Find the half-life of the material
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
A%28t%29=6000e%5E%28-.05t%29
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(A)Find the amount present after 12 days
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This means, find A when t=12, or find A%2812%29.
A%2812%29=6000%2Ae%5E%28-0.05%2A12%29
A%2812%29=6000%2A0.5488
A%2812%29=3300, not being sure how much accuracy your given values really allow.


(B)Find the half-life of the material
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When A(t) is 3000.
3000=6000%2Ae%5E%28-0.05t%29, and you want to find this t.
1%2F2=1%2Ae%5E%28-0.05t%29
ln%281%2F2%29=ln%28e%5E%28-0.05t%29%29
ln%281%2F2%29=-0.05t%2Aln%28e%29=-.05t
t=%28-1%2F0.05%29%2Aln%281%2F2%29
t=-20%2Aln%281%2F2%29=-20%2A%28-0.693%29
t=13.9 years, or, not knowing how much accuracy is given, maybe 14 years is half life.