# Suppose the total amount, A, of radioactive material present in the atmosphere at time T can be modeled by the formula `int_0^T(Pe^(-rt))dt` , Where P is a constant and t is time in years....

Suppose the total amount, A, of radioactive material present in the atmosphere at time T can be modeled by the formula `int_0^T(Pe^(-rt))dt` , Where P is a constant and t is time in years. Suppose that recent research suggests that r=0.002 and P (present amount of radioactive material) = 200 millirads. Estimate the total future buildup of radioactive material in the atmosphere if r and P were to remain constant.

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Assuming future represents a time T=oo

Amount of radioactivity,

` A=int_0^TP*e^(-rt)dt`

`=P*int_0^Te^(-rt)dt`

`=-P/r[e^(-rt)]_0^T`

`=-200/0.002[e^(-0.002*oo)-e^(-0.002*0)]`

`=-100000*-1`

`=100000 millirads`

`=100000 millirads*(1rad)/(1000millirads)`

`=100 rads`

Therefore, total future buildup of radioactive material in the atmosphere is 100 rads.