Question

When a certain drug enters the blood stream, its potency decreases exponentially with a half life of 6 hours. Suppose the initial amount of the drug present is A (sub 0). How much of the drug will be present after each number of hours?
a. 6 b. 24 c. t


Thank you so much for your help!


When a certain drug enters the blood stream, its potency decreases exponentially with a half life of 6 hours. Suppose the initial amount of the drug present is A (sub 0). How much of the drug will be present after each number of hours?
a. 6 b. 24 c. t

Amount=Ao* (1/2)^t/6 is one way to solve the question. Another is

Amount=Ao*e^(-.692t/6)
where t is time.


no clue


Let A be the amount left after time t, thus we have A(t). We're told this is a negative exponential of the form Ke^(-rt) where r is the rate of decrease and t is the time. K is an arbitrary constant that needs to be determined. So we have
(1) A(t)=Ke^(-rt)=Ke^(-rt)
When t=0, K = the amount entered. When t=6, A=(1/2)K=Ke^(-r*6), so
1/2=e^(-r*6) or ln(1/2)=-6r or
r=(-1/6)*ln(1/2)
If you use this in (1) you'll get
A(t)=Ke^(-(-1/6)*ln(1/2)
*t) or
(2) A(t)=K*(1/2)^((1/6)*t)
Now answer the questions. Always test t=0 and the number that gives the first half-life. For t=0, A(t)=K and for t=6, A(t)=(1/2)K
This is a gerneral way to solve exponential problems.
I'll let you finish it.