to determine whether a person has as thyroid deficiency, a radioactive iodine with a half-life of 8.2 days is injected into the bloodstream. a healthy thyroid is able to absorb all of the radioactivity. the amount, R, of radioactivity present after t days can be modeled by the relationship R(t) = Ro (1/2)^t/8.2, where Ro is the initial dose. how much iodine has been absorbed into a health person's body after 48 hours?

Question

to determine whether a person has as thyroid deficiency, a radioactive iodine with a half-life of 8.2 days is injected into the bloodstream. a healthy thyroid is able to absorb all of the radioactivity. the amount, R, of radioactivity present after t days can be modeled by the relationship R(t) = Ro (1/2)^t/8.2, where Ro is the initial dose. how much iodine has been absorbed into a health person's body after 48 hours?

Answer 1

48 hours = 2 days

What is Ro?

Answer 2

To find out how much iodine has been absorbed into a healthy person's body after 48 hours, we need to substitute the given values into the equation R(t) = Ro (1/2)^(t/8.2).

First, let's convert 48 hours to days by dividing it by 24 since there are 24 hours in a day:
48 hours / 24 hours/day = 2 days

Now, we can substitute the values into the equation:
R(t) = Ro (1/2)^(t/8.2)
R(2) = Ro (1/2)^(2/8.2)

Since the initial dose (Ro) is not given in the question, we cannot provide an absolute answer. However, we can calculate the amount relative to the initial dose. Let's assume the initial dose is 100 units for demonstration purposes:

R(2) = 100 (1/2)^(2/8.2)

Now, simplify the equation:

R(2) = 100 (1/2)^(0.2439)

To evaluate (1/2)^(0.2439), raise 1/2 to the power of 0.2439 using a calculator or mathematical software:

(1/2)^(0.2439) ≈ 0.8763

Now, substitute this value back into the equation:

R(2) = 100 * 0.8763 ≈ 87.63 units

So, after 48 hours, approximately 87.63 units of iodine have been absorbed into a healthy person's body assuming the initial dose is 100 units.