Answer to Question #329798 in Differential Equations for ben

Question

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

Answer 1

$dA/dt =-0.0004332$

$\int dA=\smallint -0.0004332 dt$

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