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

`200((1)/(2))^x< 1`

Step-by-step 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((1)/(2))`

After 2 hours, the amount =
`(200((1)/(2)))/(2)=200((1)/(2))^2`

After 3 hours, the amount =
`200((1)/(2))^3`

....... so on,

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

`A(t) = 200((1)/(2))^t`

If A(t) < 1 mg

`\implies 200((1)/(2))^x< 1`

Which is the required inequality..