Question

The amount of a drug in a person's bloodstream can be modeled with exponential decay. Suppose that, in 3 hours, 18% of the drug is removed from the bloodstream. What is the half-life of the drug?
A) 8.1 hours
B) 8.7 hours
C) 9.3 hours
D) 9.9 hours
E) 10.5 hours

Answer 1

E. Use the exponential decay formula

Answer 2

Can you show me how to set it up?

Answer 3

first write the formula for exponential decay:
I'm going to use my own variables for convience

F=Ae^(kt)

Answer 4

F=amount you have
A=amount you start with
k=constant
t=time elapsed

Answer 5

what you have to do first is find k, so using 3 hours and 18% we find k

Answer 6

assume you start with 100% so A=1
F=1-.18=.82 <---- this is cause you remove .18 from the blood, leaving you with .82

Answer 7

so you have .82=1e^(3k)

Answer 8

solve for k

Answer 9

then plug k into the equation. this time F=.5 since you are left with half the amount and t is what you are trying to find.

Answer 10

and that give me 10.5?

Answer 11

how do I solve for K? im sorry

Answer 12

.82=1e^(3k)

Ln(.82)=3k
k=Ln(.82)/3