Please show me how to solve:
Doctors can use radioactive iodine to treat some forms of cancer. The half-life of iodine - 131 is 8 days. A patient receives a treatment of 12 millicuries of iodine - 131. (A mullicurie is a unit of radioactivity.) How much iodine - 131 remains in the patient 16 days later?
amount = 12 (1/2)^(168)
= 12(1/2)^2 = 3 millicuries
To solve this problem, we need to understand the concept of half-life and use the formula to calculate the remaining radioactive material.
The half-life of a radioactive substance is the time it takes for half of the initial quantity to decay. In this case, the half-life of iodine-131 is 8 days.
To determine how much iodine-131 remains in the patient's body after 16 days, we can follow these steps:
Step 1: Determine the number of half-lives that have passed.
To find the number of half-lives, we divide the given time by the half-life:
Number of half-lives = Time passed / Half-life
In this case, the time passed is 16 days, and the half-life is 8 days, so:
Number of half-lives = 16 days / 8 days = 2 half-lives
Step 2: Calculate the remaining amount of iodine-131.
We use the formula: Remaining amount = Initial amount × (1/2)^(number of half-lives)
In this case, the initial amount is 12 millicuries:
Remaining amount = 12 millicuries × (1/2)^(2 half-lives)
Remaining amount = 12 millicuries × (1/2)^2
Remaining amount = 12 millicuries × (1/4)
Remaining amount = 3 millicuries
Therefore, after 16 days, the patient will have approximately 3 millicuries of iodine-131 remaining in their body.