Question
In nuclear medicine, a radioactive isotope is used to diagnose certain diseases. A particular isotope has a half-life of 6 hours, which means that every 6 hours, the amount of radioactive isotope is reduced by half due to radioactive decay. In one procedure, 2 milligrams (mg) of the isotope is injected into the patient. Determine: a) Express the remaining amount of the radioactive isotope as a function of time using a logarithmic exponential function. b) Determine the amount of isotope that will remain in the patient's body after 24 hours.
176
likes882 views
Answer to a math question In nuclear medicine, a radioactive isotope is used to diagnose certain diseases. A particular isotope has a half-life of 6 hours, which means that every 6 hours, the amount of radioactive isotope is reduced by half due to radioactive decay. In one procedure, 2 milligrams (mg) of the isotope is injected into the patient. Determine: a) Express the remaining amount of the radioactive isotope as a function of time using a logarithmic exponential function. b) Determine the amount of isotope that will remain in the patient's body after 24 hours.
Lurline
4.6103 Answers
**Step a:**
Given exponential decay function:
A(t) = A_0 \times \left(\frac{1}{2}\right)^{\frac{t}{h}}
For the isotope with a half-life of 6 hours:
A(t) = 2 \times \left(\frac{1}{2}\right)^{\frac{t}{6}}
A(t) = 2 \times 2^{-\frac{t}{6}}
**Step b:**
To find the amount of the isotope remaining after 24 hours:
A(24) = 2 \times 2^{-\frac{24}{6}}
A(24) = 2 \times 2^{-4}
A(24) = 2 \times \frac{1}{16}
A(24) = \frac{2}{16}
A(24) = \frac{1}{8}
**Answer:**
After 24 hours,0.125
Given exponential decay function:
For the isotope with a half-life of 6 hours:
**Step b:**
To find the amount of the isotope remaining after 24 hours:
**Answer:**
After 24 hours,
Frequently asked questions (FAQs)
What is the derivative of sin(x^2) using the chain rule?
+
What is the scalar product of vector A = [3, 5] and vector B = [2, -4]?
+
What is the sum of the interior angles of a 15-sided polygon?
+
New questions in Mathematics