Question #329798

Suppose that 𝑑𝐴 𝑑𝑡 = −0.0004332 𝐴(𝑡) represents a mathematical model for the radioactive decay of radium – 226, where 𝐴(𝑡) is the amount of radium (measured in grams) remaining at time 𝑡 (measured in years). How much of the radium sample remains at the time 𝑡 = −0.002 with initial condition 𝐴(1) = 0.005


1
Expert's answer
2022-04-17T08:59:03-0400

dA/dt=0.0004332dA/dt =-0.0004332

dA=0.0004332dt\int dA=\smallint -0.0004332 dt

A(t)=-0.0004332t +C

A(1)=0.005=-0.0004332x1+C

C=0.0054332

A(-0.002)=-0.0004332x(-0.002)+0.0054332=0.005434





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