an accident at a nuclear power plant has left the surrounding area polluted with

Question

an accident at a nuclear power plant has left the surrounding area polluted with radioactive material that undergoes natural decay. The initial amount of radioactive material present is 15 safe units and 5 months later it is 10 safe units.

a.) write a fromula giving the amount A9t) of radioactive material (in safe units) remianing after t months

b.) what amount of radioactive material will remain after 8 months?

c.) how long- total number of months or fraction thereof- will it be until A(t)= 1 safe unit, so it is safe for people to return to the area?

Explanation / Answer

A = A0 e^(-lambda t)

10 = 15*e^(-lambda*5)

lambda = 0.081

so A(t) = 15*e^(-0.081*t)

b) 15*e^(-0.081*8)=7.84

c) 1 = 15*e^(-0.081*t)

solve for t

t=33.43 months

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