Question

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

Answer 1

Answer:

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 × $(1-\dfrac{\textrm rate}{100})^{\textrm time}$

I.e f = i × $(1-\dfrac{\textrm r}{100})^{\textrm t}$

Or, 40 mg = 200 mg × $(1-\dfrac{\textrm 15}{100})^{\textrm t}$

Or, $\dfrac{40}{200}$ = $(1-\dfrac{\textrm 15}{100})^{\textrm t}$

Or , 0.2 = $(\frac{100 - 15}{100})^{t}$

Or,  $(\frac{85}{100})^{t}$ = 0.2

Taking Log both side

So, $Log_{10}$ $(\frac{85}{100})^{t}$ = $Log_{10}$0.2

Or, t ×  $Log_{10}$0.85 =  $Log_{10}$0.2

Or, t (-0.07) = - 0.69

∴  t = $\dfrac{.69}{.07}$

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