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

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Part 1
The amount remaining after 10 days is
  
enter your response here millicuries.

Answer 1

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.