Question

please show answer before and after rounding

Finding the rate or time in a word problem on continuous... The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 9.1% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Note: This is a continuous exponential decay model. Do not round any intermediate computations, and round your answer to the nearest hundredth. days X ?

Answer 1

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Since the decoy rate posametin is g.1% þess day, bo can take the model as, - 0.091t A(H) = Age timet w where, A(T) = Amount remaining often Ao = Initial amount Now when A(t) = A to, then we have, Aoe roogit 1/2 Ao 0.01 => e S st > b (e-oogit) = ln (%) -> -0.09 its In (12) Pm (42) >>> ES- 0.031 0.091 >>to Tn (2) Il(%) = -2(23] => t = [7.62 days (sounded to nearest handelin

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So we have,

Exact Answer : ln(2)/0.091 days

Answer (after rounding off to nearest hundredth) : 7.62 days