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The function A = Ape-0.0099x models the amount in pounds of a particular radioactife material stored in a concrete vault, where x is the numberof years since the material was put into the vault. How many years will it be until 30% of the original amount remains in the vault? Round off tothe nearest year.

Respuesta :

Solution

we have the following equation:

[tex]A=A_pe^{-0.0099x}[/tex]

For this case we can do this:

[tex]0.3A_p=A_pe^{-0.0099x}[/tex]

We can cancel in both sides Ap and then we can apply natural log and we got:

[tex]\ln (0.3)=-0.0099x[/tex]

Solving for x who represent t we got:

[tex]x=\frac{\ln (0.3)}{-0.0099}=121.61[/tex]

Rounded to the nearest year we got:

121yr

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