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) = Iert

alright
so equation is
[tex]A(t)=Pe^{rt}[/tex]
P=initial amount
and t=time
r=rate

given
initial amount is 50
rate is 10%, but decreasing by 10% so -0.1
and time=6

[tex]A(6)=50e^{-0.1*6}[/tex]
[tex]A(6)=50e^{-0.6}[/tex]
A(6)=27.4406
about 27mg

Answer Link

aksnkj aksnkj · Answer 2 · 2021-11-09T10:37:12+01:00

The amount of medicine decreases exponentially in the bloodstream. The amount of medicine remaining in the bloodstream after 6 hours is 27.44 mg.

Given:

The initial amount of medicine given to the patient is [tex]I=50[/tex] mg.

The rate at which the medicine is leaving the bloodstream is, [tex]r=-10\%=-0.1[/tex] (negative sign represents decrement in the amount).

It is required to find the remaining amount of medicine in the bloodstream after [tex]t=6[/tex] hours.

So, use the formula of depreciation to find the remaining amount A(t) as,

[tex]A(t) = Ie^{rt}\\A(t)=50\times e^{-0.1\times 6}\\A(t)=27.44[/tex]

Therefore, the amount of medicine remaining in the bloodstream after 6 hours is 27.44 mg.

For more details, refer to the link:

https://brainly.com/question/15261812