Respuesta :
The amount of medicine that will remain in the system after 6 hours is 27.44 milligrams.
Given to us
Initial condition = 50 milligrams of medicine,
Rate at which medicine will be disposed = 10% = 0.1
function = [tex]A(t) = I \times e^{rt}[/tex]
To find
Medicine remains in the system after 6 hours
As the function is already given to us, substituting the values in the function we get,
[tex]A(t) = I \times e^{rt}[/tex]
[tex]A(t) = (50) \times e^{(-0.1\times 6)}[/tex]
the value of r is -0.1(10%) because the medicine is leaving the system, therefore, the value of medicine will be reduced.
Solving the function further,
[tex]A(t) = (50) \times e^{(-0.1\times 6)}\\A(t) = 27.44\ milligrams[/tex]
Hence, the amount of medicine that will remain in the system after 6 hours is 27.44 milligrams.
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