Question

Radioactive technetium-99m is often used in diagnostic medicine because it has relatively short half-life but lasts long enough to get the needed testing done on the patient. If its half-life is 6 hours, how much of the radioactive material from a 2.5ml injection will be in the body in 30 hours? Write your answer rounded to nearest hundredth.

Answer 1

Using an exponential function, it is found that 0.08 ml of the will be in the body in 30 hours.

The amount of a decaying substance is modeled by an exponential function in the following format:

$A(t) = A(0)e^{-kt}$

In which:

• A(0) is the initial amount.
• k is the decay rate, as a decimal.

In this problem, the half-life is 6 hours, which means that $A(6) = 0.5A(0)$, and this is used to find k.

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-6k}$

$e^{-6k} = 0.5$

$\ln{e^{-6k}} = \ln{0.5}$

$-6k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{6}$

$k = 0.11552453009$

Hence:

$A(t) = A(0)e^{-0.11552453009t}$

2.5 ml injection, hence $A(0) = 2.5$

After 30 hours, we have to find A(30), hence:

$A(t) = 2.5e^{-0.11552453009t}$

$A(30) = 2.5e^{-0.11552453009(30)}$

$A(30) = 0.08$

0.08 ml of the will be in the body in 30 hours.

A similar problem is given at https://brainly.com/question/16984805