Question

a 100lb block of uranium is decaying into lead exponentially using the equation Q(t)=Q e^kt. if 85 lbs remains after 5 years how many years will there be 10 lbs or uranium?

Answer 1

is this a plug and play situation?

Answer 2

i havent really read the question, but that's my first guess.

Answer 3

Q(t)=Q*e^(kt)


Q(t)=100*e^(kt)


85=100*e^(k*5)


85/100=e^(k*5)


0.85=e^(k*5)


ln(0.85)=5k


ln(0.85)/5=k


-0.0325 = k


k = -0.0325

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Q(t)=100*e^(kt)


Q(t)=100*e^(-0.0325t)


10=100*e^(-0.0325t)


10/100=e^(-0.0325t)


0.1=e^(-0.0325t)


ln(0.1)=-0.0325t


ln(0.1)/(-0.0325) = t


70.8488= t


t = 70.8488


So in approximately 70.8488 years, there will be 10 lbs of uranium left.