The decay of 942 mg of an isotope is described by the function A(t)= 942e-0.012t, where t is time in years. Find the amount left after 71 years. Round your answer to the nearest mg.

Respuesta :

[tex]\bf A(t)=942e^{-0.012t}\qquad \boxed{\stackrel{\textit{after 71 years}}{t=71}}\qquad \qquad A(t)=942e^{-0.012(71)} \\\\\\ A(t)\approx 401.82042087707606813879[/tex]

Applying the exponential function, it is found that the amount after 71 years is of 402 mg.

The exponential equation for the amount after t years is given by:

[tex]A(t) = 942e^{-0.012t}[/tex]

For the amount after 71 years, we find A(71), thus:

[tex]A(71) = 942e^{-0.012(71)} = 402[/tex]

The amount after 71 years is of 402 mg.

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