The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of the original dosage? Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve.

It will take 4.84 hours for the drug to decay to 93% of the original dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is:

Now, we know that A becomes half after 47 hours which means that;

Using this in the above equation we get;

 where t = 47 hours

Taking log on both sides we get;

k = -0.015

Now, the time it will take for the drug to decay to 93% of the original dosage is given by;

 where t is the required time

Taking log on both sides we get;

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.

ok

step-by-step explanation: