Doctors can use radioactive chemicals to treat some forms of cancer. The half life of a certain chemical is 5 days. A patient receives a treatment of 28 millicuries of the chemical. (A millicurie is a unit of radioactivity.) How much of the chemical remains in the patient 10 days later?
Question content area bottom
Part 1
The amount remaining after 10 days is
enter your response here millicuries.
To find out how much of the chemical remains in the patient 10 days later, we need to determine the decay of the chemical over time.
The decay of a radioactive substance follows an exponential decay model, which can be represented by the formula:
A = A0 * (1/2)^(t/h)
Where:
A = amount remaining
A0 = initial amount
t = time elapsed
h = half-life of the substance
In this case, the initial amount (A0) is 28 millicuries, the time elapsed (t) is 10 days, and the half-life (h) is 5 days. Plugging in these values into the formula, we get:
A = 28 * (1/2)^(10/5)
Simplifying this expression, we have:
A = 28 * (1/2)^2
A = 28 * (1/4)
A = 7
Therefore, the amount remaining in the patient 10 days later is 7 millicuries.