Question

"The half-life of a certain tranquilizer in the bloodstream is 33 hours. How long will it take for the drug to decay to 93% of the original dosage? Use the exponential decay

model, A = Ag ekt, to solve.hours
(Round to one decimal place as needed.)

Answer 1

To determine the time it takes for a tranquilizer to decay to 93% of its original dosage using the exponential decay model and its half-life of 33 hours, the decay constant is first found, and then the time is calculated by rearranging and solving the exponential decay equation.

Step-by-step explanation:

The question involves solving for the time it takes for a tranquilizer with a certain half-life to decay to a specific percentage using the exponential decay model.

In this case, we use the formula A = A0ekt, where A is the final amount of the drug, A0 is the initial amount, e is the base of the natural logarithm, k is the decay constant, and t is the time in hours.

The decay constant (k) can be found using the half-life formula k = -0.693/t1/2. We know the half-life t1/2 is 33 hours, and we are looking for the time when the tranquilizer has decayed to 93% of its original amount, meaning A = 0.93A0.

Setting up the equation 0.93A0 = A0e(-0.693/33)t and solving for t, we find the time it takes for the drug to decay to 93% of the original dosage.