The radioactive isotope thorium 234 has a halflife of approx

The radioactive isotope thorium 234 has a half-life of approximately 578 hours. If a sample has a mass of 62 milligrams, find an expression for the mass after t hours. Q(t)= How much will remain after 75 hours? (Round your answer to one decimal place.) mg When will the initial mass decay to 19 milligram? (Round your answer to one decimal place.) hr A culture of bacteria triples after 6 hours. What proportion of the original number of bacteria Q_0 will be present after 12 hours? Q(12)=

Solution

decay constant = 0.693/ half life = 0.693/578

Q(t) = Qoe^-kt

a) Q(t) = 62e^(-0.00119t)

b) after 75 hrs t = 578 hrs

Q(75) = 62e^(-0.00119*578) =62*0.5026 = 31.16 = 31.2 mg

c) Q(t) = 19mg ; find t

19 = 62e^(-0.00119t)

0.306 =e^(-0.00119t)

take ln on both sides:

ln(0.306) = -0.00119t

t = 993.86 = 993.9 hrs