Answer:
[tex]200(\frac{1}{2})^x< 1[/tex]
Explanation:
Given,
The original amount of the medicine in the body = 200 mg,
If the amount of medicine in his body will be one half of the amount from the previous hour.
Then the amount of the medicine after 1 hour = [tex]200(\frac{1}{2})[/tex]
After 2 hours, the amount = [tex]\frac{200(\frac{1}{2})}{2}=200(\frac{1}{2})^2[/tex]
After 3 hours, the amount = [tex]200(\frac{1}{2})^3[/tex]
....... so on,
Thus, after t hours the amount ( say A(t) )
[tex]A(t) = 200(\frac{1}{2})^t[/tex]
If A(t) < 1 mg
[tex]\implies 200(\frac{1}{2})^x< 1[/tex]
Which is the required inequality..
