Answer:
(a)25 Milligrams
(b)15%
(c)[tex]A(10) = 25(0.85)^{10}[/tex]
Step-by-step explanation:
The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:
[tex]A(t) = 25(0.85)^t[/tex]
(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.
(b)From the model,
[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]
We can also use this method:
[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]
We can see that for every hour, 15% of the drug leaves the body.
(c)After 10 hours
When t=10
[tex]A(10) = 25(0.85)^{10}[/tex]
The amount of drug left after 10 hours is given above in function notation.
