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

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 mg.

The rate at which the medicine is leaving the bloodstream is, (negative sign represents decrement in the amount).

It is required to find the remaining amount of medicine in the bloodstream after hours.

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

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

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