Question

Please answer #8 and #9. Thank You!

The concentration of a drug in grams/cubic centimeter (g/cm3) t min after it has been injected into the bloodstream is given by the following where a, b, and k are positive constants, with b > a. C(t) = k/b - a(e-at - e-bt) At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run? A radioactive substance decays according to the formula below where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant. Q(t) = Q0e-kt Find the half-life of the substance in terms of k. Suppose that a radioactive substance decays according to the formula Q(t) = 21e-0.0001591t How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.) yr

Show transcribed image text The concentration of a drug in grams/cubic centimeter (g/cm3) t min after it has been injected into the bloodstream is given by the following where a, b, and k are positive constants, with b > a. C(t) = k/b - a(e-at - e-bt) At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run? A radioactive substance decays according to the formula below where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant. Q(t) = Q0e-kt Find the half-life of the substance in terms of k. Suppose that a radioactive substance decays according to the formula Q(t) = 21e-0.0001591t How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.) yr