Question

Finn takes 200 milligrams of medicine. Each hour, the amount of medicine in his body will be one half of the amount from the previous hour.Use the drop-down menus to complete an inequality that can be solved to find how much time, t, it will take for there to be less than 1 milligram of medicine remaining in Finn’s body.

Answer 1

Answer:

$200(\frac{1}{2})^x< 1$

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 = $200(\frac{1}{2})$

After 2 hours, the amount = $\frac{200(\frac{1}{2})}{2}=200(\frac{1}{2})^2$

After 3 hours, the amount = $200(\frac{1}{2})^3$

....... so on,

Thus, after t hours the amount ( say A(t) )

$A(t) = 200(\frac{1}{2})^t$

If A(t) < 1 mg

$\implies 200(\frac{1}{2})^x< 1$

Which is the required inequality..