# Math Help - decay rate of drug

1. ## decay rate of drug

This problem is long, no idea how to start this..plz help
Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anestheized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbital is eliminated exponentially from the dog's bloodstream, with a half-life of 5 h. what single dose should be adminstered in order to anesthetize a 50-kg dog for 1 h?

2. Originally Posted by DMDil
This problem is long, no idea how to start this..plz help
Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anestheized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbital is eliminated exponentially from the dog's bloodstream, with a half-life of 5 h. what single dose should be adminstered in order to anesthetize a 50-kg dog for 1 h?
Substitute $x = \frac{1}{2} x_0$ and t = 5 into $x = x_0 e^{kt}$ and solve for k. So:

$x = x_0 e^{\left(-\frac{\ln 2}{5}\right) t}$.

Substitute $x = (45)(50)$ and $t = 1$ and solve for $x_0$.