⅔ and 8/12 form a proportion.
<span>x^2+10x + 25 = (x + 5)^2
missing = 25
hope it helps</span>
Answer:
14
Step-by-step explanation:
answer is 14 trust me
All you have to do is plug in the given values into the given equation and evaluate.
The expression is,
![A(t) = l{e}^{rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20%20l%7Be%7D%5E%7Brt%7D%20)
But we have to analyze the problem carefully. This is a natural phenomenon that can be modelled by a decay function. The reason is that, after every hour we expect the medicine in the blood to keep reducing.
Therefore we use the decay function rather. This is given by,
![A(t) = l{e}^{-rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20%20l%7Be%7D%5E%7B-rt%7D)
where,
![l = 100 \: milligrams](https://tex.z-dn.net/?f=l%20%3D%20100%20%5C%3A%20milligrams)
![r = \frac{14}{100} = 0.14](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B14%7D%7B100%7D%20%20%3D%200.14)
and
![t = 10 \: hours](https://tex.z-dn.net/?f=t%20%3D%2010%20%5C%3A%20hours)
On substitution, we obtain;
![A(10) = 100 \times {e}^{ - 0.14 \times 10}](https://tex.z-dn.net/?f=A%2810%29%20%3D%20%20100%20%5Ctimes%20%7Be%7D%5E%7B%20-%200.14%20%5Ctimes%2010%7D%20)
![A(10) = 100 \times {e}^{ - 1.4}](https://tex.z-dn.net/?f=A%2810%29%20%3D%20%20100%20%5Ctimes%20%7Be%7D%5E%7B%20-%201.4%7D%20)
Now, we take our calculators and look for the constant
![e](https://tex.z-dn.net/?f=e)
,then type e raised to exponent of -1.4. If you are using a scientific or programmable calculator you will find this constant as a secondary function. Remember it is the base of the Natural logarithm.
If everything goes well, you should obtain;
![A(10) = 100 \times 0.24659639](https://tex.z-dn.net/?f=A%2810%29%20%3D%20%20100%20%5Ctimes%200.24659639)
This implies that,
![A(10) = 24.66](https://tex.z-dn.net/?f=A%2810%29%20%3D%20%2024.66)
Therefore after 10 hours 24.66 mg of the medicine will still remain in the system.