please solve this problem and explain this to me. We use this formula A(t)=P(1+r

Question

please solve this problem and explain this to me. We use this formula A(t)=P(1+r)^t

The half life of a decaying substance is the amount of time it takes for the substance to reduced to half of its original amount. If a substance has a half life of 800 years, and there are 30 mg present now, how long will it take for the substance to be reduced to 10 mg?

it will take___ years

Explanation / Answer

Dear Student Thank you for using Chegg !! Given formulae A (t) = P (1 + r)^t Also given a substance with half life = 800 years => A(800) = P/2 P/2 = P (1+ r)^800 0.5 = (1 + r)^800 (1 + r) = 0.9991339 r = -0.000866 Present quantity P = 30 mg => Final Amount = 10 mg 10 = 30 (0.9991339)^t 0.333333 = (0.9991339)^t Taking natural log both sides -1.09861 = -000866t t = 1267.97 Hence time taken for amount to reduce to 10 mg is 1268 years Solution

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