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AdrianBrewer8168
19.12.2019 •
Mathematics
You ingest 200 mg of medicine and your body removes 15% of it per hour. how long until there is only 40 mg left?
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Ответ:
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}](/tpl/images/0425/5968/bd5fe.png)
I.e f = i ×![(1-\dfrac{\textrm r}{100})^{\textrm t}](/tpl/images/0425/5968/f2d58.png)
Or, 40 mg = 200 mg ×![(1-\dfrac{\textrm 15}{100})^{\textrm t}](/tpl/images/0425/5968/4b6b9.png)
Or,
= ![(1-\dfrac{\textrm 15}{100})^{\textrm t}](/tpl/images/0425/5968/4b6b9.png)
Or , 0.2 =![(\frac{100 - 15}{100})^{t}](/tpl/images/0425/5968/1b398.png)
Or,
= 0.2
Taking Log both side
So,![Log_{10}](/tpl/images/0425/5968/f4d24.png)
=
0.2
Or, t ×
0.85 =
0.2
Or, t (-0.07) = - 0.69
∴ t =![\dfrac{.69}{.07}](/tpl/images/0425/5968/3aecb.png)
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
Ответ:
Option B is the correct option.
Step-by-step explanation:
We know that the vertex form of a quadratic's equation is generally expressed as
y = a(x - h)² + k
where (h, k) is called the vertex of the quadratic function
In our case, given the function
now comparing the equation with y = a(x - h)² + k
Here:
h = -3
k = 25/2
Therefore, the vertex of the function
is:
(h, k) = (-3, 25/2)
Thus,
The
form most quickly reveals the vertex.
Hence, option B is the correct option.