You ingest 200 mg of medicine and your body removes 15% of it per hour. how long until there is only 40 mg left?

The time after which only 40 mg of medicine left inside body is 9.8 hours

Step-by-step explanation:

Given as :

The initial quantity of medicine ingest in body = i=200 mg

The final quantity of medicine in body = f= 40 mg

The rate at which body remove medicine = r = 15%

Let The time taken to remove = t hours

According to question

The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body ×

I.e f = i ×

Or, 40 mg = 200 mg ×

Or, =

Or , 0.2 =

Or,   = 0.2

Taking Log both side

So, = 0.2

Or, t ×  0.85 =  0.2

Or, t (-0.07) = - 0.69

∴  t =

I.e t = 9.8 hours

So, The time after which only 40 mg left inside body = t = 9.8 hours

Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer