Exponential decay

Question

Doctors can use radioactive chemicals to treat some forms of cancer. The half life of a certain chemical is 8 days A patient receives a treatment of 12 millicuries of the chemical (A millicurie is a unit of radioactivity) How much of the chemical remains in the patient 16 days later?

Answer 1

Half-life is the key to this question!

The half-life of the chemical is given as 8 days, which means that after every 8 days, the amount of the chemical is halved.

The number of half-lives that have occurred in the 16-day period:

Number of half-lives = (time elapsed) / (half-life) Number of half-lives = 16 days / 8 days Number of half-lives = 2

Since two half-lives have occurred, the amount of the chemical remaining can be calculated as:

Remaining amount = Initial amount * (1/2)^(number of half-lives)

Given that the initial amount is 12 millicuries, we can substitute the values into the equation:

Remaining amount = 12 millicuries * (1/2)^2 Remaining amount = 12 millicuries * (1/4) Remaining amount = 3 millicuries

Therefore, 16 days later, there will be approximately 3 millicuries of the radioactive chemical remaining in the patient's body.

Answer 2

The patient starts with 12 millicuries.

1. At 8 days, the patient has 1/2 as much: (1/2) × (12) = 6 millicuries
2. At 16 days, 8 more days have passed, so the patient has half of what she had at 8 days, (1/2) × (6) = 3 millicuries.

The equation is:

A(t) = 12·(1/2)^t/8

Where:

1. A(t) is the amount of chemical left after t days
2. 12 is the initial amount of chemical
3. t = days

You can also plug in t = 8, then t = 16 to get the answers.