Question

If a hospital patient is given 50 milligrams of medicine, which leaves the bloodstream at 10% per hour, how many milligrams of medicine will remain in the system after 6 hours? Use the function A(t) = Ie^(rt).

Answer 1

27.44 mg

EXPLANATION :

From the problem, we have the function :

`A\left(t\right)=Ie^(rt)`

where I = initial amount

e = euler's constant

r = rate

t = time

We have :

I = 50 mg

r = -10% or 0.10 (Negative because this amount leaves the bloodstream)

t = 6 hours

The amount of medicine after 6 hours is :

`\begin{gathered} A\left(6\right)=50e^(-0.10\left(6\right)) \\ A\left(6\right)=27.44 \end{gathered}`

The answer is 27.44 mg