Question

NEED HELP PLSSS!!

You go to the doctor and he gives you 17 milligrams of radioactive dye. After 16 minutes, 6.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm.

If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived?

Give your answer to the nearest minute.

You will spend
_ minutes at the doctor's office.

Answer 1

AI-generated answer

To determine how long your visit to the doctor will take, we need to calculate the rate at which the dye is leaving your system.

We know that after 16 minutes, 6.25 milligrams of dye remain in your system. This means that in 16 minutes, 17 - 6.25 = 10.75 milligrams of dye have left your system.

To find the rate at which the dye is leaving your system, we can divide the amount of dye that leaves in 16 minutes by the time it takes: 10.75 milligrams / 16 minutes = 0.671875 milligrams per minute.

Since the radiation detector will sound the alarm if more than 2 milligrams of dye are in your system, we can set up an equation to find out how long it will take for the dye level to reach 2 milligrams.

Let x represent the number of minutes it takes for the dye level to reach 2 milligrams.

Starting with 17 milligrams and subtracting 0.671875 milligrams per minute for x minutes should equal 2 milligrams: 17 - 0.671875x = 2.

Now, we can solve for x:

17 - 0.671875x = 2.

Subtracting 17 from both sides gives us: -0.671875x = -15.

Dividing both sides by -0.671875 gives us: x = -15 / -0.671875.

Therefore, x ≈ 22.37.

Since we are rounding to the nearest minute, the answer is approximately 22 minutes.

So, your visit to the doctor's office will take approximately 22 minutes.